Your query never return any result! because of your terms which are always false!
for not in you can use join, that's more optimize!
String query = "select patient_id, contact_id, 1, '2013-12-05', NULL, patient_id from nfc_careplan_contacts a left join nfc_DeliveryPlan b on a.contact_id = b.contact_id where a.contact_id = 420 and b.contact_id = 420 and a.contact_id != b.contact_id) and a.contact_id = 420;";
Cursor c = database.rawQuery(query, null);