What was found
AIRCRAFT GROUNDED, AT FL370 IN CRUISE IAS DISAGREE: AIRSPEED ON CAPTS DECREASED TO 120KTS, F/O WAS IN RED BAND, CAPTS ALTITUDE BEGAN CLIMB, F/O BEGAN DESCENT (STBY A/S AND ALT INDICATED NORMAL AT ALL TIMES). RAN QRC & QRH PROCEDURE. AN EMERGENCY WAS DECLARED AND AIRCRAFT RETURNED TO MIA, LANDED SAFELY WITHOUT FURTHER INCIDENT. R & R CAPT PITOT PROBE PER AMM 34-11-01 WITH NEW CONNECTOR. SATISFACTORY HEATER, LEAK & RESISTANCE CHECKS, PER WDM 30-31-11/30-31-12. R & R FCC-A PER AMM 22-11-33. R & R NR 1 DEU PER AMM 31-62-21. APU SHUTDOWN AFTER A FEW MINUTES, REPLACED APU INLET PRESSURE SENSOR PER AMM 49-52-31, OPS CHECK NORMAL. ACCOMPLISHED BITE CHECK, PER AMM 49-61-00, NO FAULTS NOTED. OK FOR SERVICE.