The P fare is a KUP, so I'd assume that the P fare would be cheapest whenever only coach inventories above K remain available for sale.

This is also, by the way, one of my favorite ways to travel to Chicago. Buy two one-way tickets, get off at ORD on the outbound (as long as you don't do this too often) and drive to MKE on the return, skipping the zoo that is landside at ORD.