When one Contact is listed in more than one area; setting the contact's Priority in one area sets it for both areas.
If you want the Contact to have a different Priority in one area than the other, remove one of the Contact entries and then add the Contact back. For instance: Masood Basari is both an Emergency and Billet Contact for one student. Currently, he is Priority 3 under Emergency and also 3 under Billet. You want him to be 4 under Emergency. Delete Masood from the Emergency list. Add him back. You can now set his Emergency Priority to 4.