DURING ROLLOUT, THE CAPTAIN APPLIED BRAKES TO DECELERATE THE AIRPLANE AS IT WAS TURNING TOWARDS THE TAXIWAY. THE AIRPLANE'S LEFT MAIN LANDING GEAR BRAKES, WHICH ARE NORMALLY PROTECTED BY A BRAKE ANTI-SKID SYSTEM, LOCKED THREE OF THE FOUR WHEELS SUFFICIENTLY SO THAT THE TIRES WERE SCRUBBED DOWN AND RUPTURED. THE FOURTH TIRE WAS SCRUBBED DOWN AND DEFLATED. THE CAPTAIN STOPPED THE AIRPLANE PRIOR TO ENTERING THE TAXIWAY. POST-INCIDENT INSPECTION REVEALED CONTAMINATED ELECTRICAL CONNECTORS BETWEEN THE ANTI-SKID MANIFOLDS AND THE ANTI-SKID COMPUTER RESULTING IN THE LOSS OF ANTI-SKID PROTECTION.