Rear Tires Suddenly Lock Up Going 65

DO NOT drive this car until you get this "found" and fixed

Order of probability in my mind:

Rear axle: Something broken, loose pinion shaft, something loose floating around in there

Transmission.

Brakes. Unlikely, MIGHT indeed be a loose hardware problem. This is NOT going to be a hydraulic problem. The ONLY way that hydraulics could cause this is AFTER you have applied a LOT of pressure to the pedal, and that would be pretty rare.