Calculated columns have no ability to look forwards or backwards to other rows so you wouldn't be able to calculate priorities with just that. There are a couple of other routes that can get you there.
The easiest way I can think of to maintain a priority column would be with an Event Receiver that fires on item added, on item deleted, and on item changed. In the event receivers you would get all of the items in that list/library, sort them by score, then add the priority number.
If you're on Sharepoint 2013 or newer you could create a workflow (or Flow) that gets all the items from your list ordered by score, creates a variable "Priority" starting at 1, then loops through those items and sets Priority and increments Priority. You can set the workflow to run on create, edit, or delete. It takes quite a few steps to get that to work but it can be done.