WPF

ConversationList.Clear();

if (ConversationList == null)
{
   ConversationList = new ObservableCollection<Conversation>();
}

public void PopulateConversationList()
        {
            if (selectedContact == null)
            {
                ConversationList = null;
            }
            else
            {
                var conversations = from c in cbdc.Conversations
                                    where c.ContactID == SelectedContact.Id
                                    select c;

                if (ConversationList == null)
                {
                    ConversationList = new ObservableCollection<Conversation>();
                }
                ConversationList.Clear();

                foreach (Conversation c in conversations)
                {
                    ConversationList.Add(c);
                }


            }

public MainViewModel()
{
    ContactList = new ObservableCollection<Contact>(cbdc.Contacts);
    //Add this
    ConversationList = new ObservableCollection<Conversation>();
    //--------
    SelectedContact = ContactList.FirstOrDefault();
    PopulateConversationList();
}

public void PopulateConversationList()
{
if (selectedContact == null)
{
    //Change ConversationList = null; to this
    ConversationList.Clear();
}
else
{
    var conversations = from c in cbdc.Conversations
                        where c.ContactID == SelectedContact.Id
                        select c;

    ConversationList.Clear();

    foreach (Conversation c in conversations)
    {
        ConversationList.Add(c);
    }
}

public class MainViewModel : ViewModelBase
{
    private Contact selectedContact;

    private ObservableCollection<Contact> contactList;
    private ObservableCollection<Conversation> conversationList;

    public MainViewModel()
    {
        ContactList = new ObservableCollection<Contact>(cbdc.Contacts);
        ConversationList = new ObservableCollection<Conversation>();
        SelectedContact = ContactList.FirstOrDefault();
        PopulateConversationList();
    }

    public ObservableCollection<Contact> ContactList
    {
        get
        {
            return contactList;
        }

        private set
        {
            if (contactList != value)
            {
                contactList = value;
                RaisePropertyChanged();
            }
        }

    }

    public Contact SelectedContact
    {
        get
        {
            return selectedContact;
        }

        set
        {
            if (selectedContact != value)
            {
                selectedContact = value;
                RaisePropertyChanged();
                PopulateConversationList();
            }
        }
    }

    public ObservableCollection<Conversation> ConversationList
    {
        get
        {
            return conversationList;
        }

        private set
        {
            if (conversationList != value)
            {
                conversationList = value;
                RaisePropertyChanged();
            }
        }
    }

    public void PopulateConversationList()
    {
        if (selectedContact == null)
        {
            ConversationList.Clear();
        }
        else
        {
            var conversations = from c in cbdc.Conversations
                                where c.ContactID == SelectedContact.Id
                                select c;

            ConversationList.Clear();

            foreach (Conversation c in conversations)
            {
                ConversationList.Add(c);
            }
        }
    }
}

<Window x:Class="ContactsList.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
        xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
        mc:Ignorable="d"
        Title="MainWindow" Height="350" Width="525">
    <DockPanel LastChildFill="True">
        <ListBox x:Name="ContactsLstBx" Width="200" ItemsSource="{Binding ContactList}" SelectedItem="{Binding SelectedContact, UpdateSourceTrigger=PropertyChanged}" DockPanel.Dock="Left">
            <ListBox.ItemTemplate>
                <DataTemplate>
                    <TextBlock Text="{Binding Path=Name}" />
                </DataTemplate>
            </ListBox.ItemTemplate>
        </ListBox>
        <ListBox x:Name="ConversationLstBx" Width="200" ItemsSource="{Binding ConversationList}" DockPanel.Dock="Right" HorizontalAlignment="Right" >
            <ListBox.ItemTemplate>
                <DataTemplate>
                    <TextBlock Text="{Binding Path=Title}" />
                </DataTemplate>
            </ListBox.ItemTemplate>
        </ListBox>
    </DockPanel>
</Window>

public partial class MainWindow : Window
{
    public MainViewModel ViewModel { get; private set; }

    public MainWindow()
    {
        InitializeComponent();
        ViewModel = new MainViewModel();
        DataContext = ViewModel;
    }
}

public class MainViewModel : ViewModelBase
{<br />
    //The collections can just be auto-implemented properties since we have no reason
    //to use custom logic like PropertyChanged.  Remember, the view doesn't listen for that.
    public ObservableCollection<Contact> ContactList { get; private set; }
    public ObservableCollection<Conversation> ConversationList { get; private set; }
    private Contact selectedContact;
    public Contact SelectedContact
    {
        get
        {
            return selectedContact;
        }
        set
        {
            if (selectedContact != value)
            {
                selectedContact = value; 
                PopulateConversationList();
                RaisePropertyChanged();
            }
        }
    }
    public MainViewModel()
    {
        ContactList = new ObservableCollection<Contact>(cbdc.Contacts);
        ConversationList = new ObservableCollection<Conversation>();
        SelectedContact = ContactList.FirstOrDefault();
        //Don't need the PopulateConversationList() call because it's already called
        //when setting SelectedContact
    }

    public void PopulateConversationList()
    {
        //Just optimized the if-statement a bit since Clear() is called regardless
        ConversationList.Clear();
        if (selectedContact != null)
        {
            /*
            var conversations = from c in cbdc.Conversations
                                where c.ContactID == SelectedContact.Id
                                select c;
            */
            //My simulated database call, use your call in your application
            var conversations = cbdc.GetConversations(selectedContact);

            foreach (Conversation c in conversations)
                ConversationList.Add(c);
        }
    }
}

public class ViewModelBase : INotifyPropertyChanged
{
    protected MockDB cbdc;
    public event PropertyChangedEventHandler PropertyChanged;
    public ViewModelBase()
    {
        cbdc = new MockDB();
    }
    protected void RaisePropertyChanged([CallerMemberName] string propertyName = null) =>
        PropertyChanged?.Invoke(this, new PropertyChangedEventArgs(propertyName));
}
public class MockDB
{
    private Dictionary<Contact, List<Conversation>> conversations;
    public List<Contact> Contacts { get; private set; }
    public MockDB()
    {
        Contacts = CreateContacts();
        conversations = CreateConversations(Contacts);
    }
    public List<Conversation> GetConversations(Contact c) =>
        conversations[c];
    private List<Contact> CreateContacts()
    {
        return new List<Contact>()
        {
            new Contact("Jim"),
            new Contact("Bob"),
            new Contact("Mary")
        };
    }
    private Dictionary<Contact, List<Conversation>> CreateConversations(List<Contact> contacts)
    {
        Dictionary<Contact, List<Conversation>> conversationMap = new Dictionary<Contact, List<Conversation>>();
        foreach (Contact c in contacts)
            conversationMap.Add(c, CreateConversationList(c));
        return conversationMap;
    }
    private List<Conversation> CreateConversationList(Contact contact)
    {
        return new List<Conversation>()
        {
            new Conversation($"Hi {contact.Name}!"),
            new Conversation("Pleasant day today.")
        };
    }
}

public class Contact
{
    public string Name { get; private set; }

    public Contact(string contactName)
    {
        Name = contactName;
    }
}

public class Conversation
{
    public string Title { get; private set; }

    public Conversation(string conversationText)
    {
        Title = conversationText;
    }
}

Richard Deeming wrote:

You should also store the event handler delegate in a local variable before testing and calling it, since other threads might modify it between the null test and the invocation.

public event PropertyChangedEventHandler PropertyChanged;

protected void RaisePropertyChanged([CallerMemberName] string propertyName = null)
{
    PropertyChanged?.Invoke(this, new PropertyChangedEventArgs(propertyName));
}

Dadou55 wrote:

Also i would like to understand why when i'm clicking on the Label it recognizes it like a TextBlock.

Mouse.DirectlyOver Property (System.Windows.Input)[^]:

Controls can be composed of multiple elements. DirectlyOver reports the specific element in the composite control the mouse pointer is over and not the control itself. For example, depending on which part of a Button the pointer is over, the DirectlyOver property could report the TextBox of the Content property or the ButtonChrome.