The key is that Monty ALWAYS open a door that contains nothing, and he knows which door has the car. His action is therefore informative and alters the probabilities.
If you pick door A and Monty opens door B the odds are as follows:
1/3rd of the time the car is behind door A, and Monty randomly picks door B or C, 50% chance that he will pick either one. Monty is telling you nothing in this case.
2/3rds of the time the car is behind door B or C, and Monty has NO CHOICE in what door he opens, by opening B he is, 2/3rds of the time, telling you the car is behind C.
Thus in 2/3 cases you win by switching.
This is entirely counter-intuitive but it is nevertheless correct.
