I do not think, this code has any issue.
$post = Depress::find($post_id);
$post['like'] = $post['like'] + 1;
This should work definitely, only if $post_id has the right value (the one it presents in the DB).
What I have tried
I did check the above thing and I found this error Call to a member function save() on a non-object
when $post_id contains the id (1000) which is not present in the DB.
Please check the same (check whether id exist in DB or not) and if you still face the same issue, please typecast $post_id to integer and then check it.
I hope this will help you.