Yes, definitely. However, it's a pretty reasonable inference, because Monty would not open a door without being sure that it would not contain the prize becaus

Yes, definitely. However, it's a pretty reasonable inference, because Monty would not open a door without being sure that it would not contain the prize because that would just destroy the dramatic tension. "Oops, sorry, guess you lost. Didn't see that coming. Better luck next time."