I am not a mathematician, but I have always considered the Monty Hall trick to be more of a word trick than any basis in mathematics. Look at it this way:

If you pick one door out of a million and Monty Hall opens 999,998 others and it's between yours and the other door, there's a good chance Monty Hall knew where the car was since the chances of him doing that at random are so small, so of course your chance is better if you switch to the other door since there is a strong probability he didn't miss that one door just by chance.

On the other hand, if Monty opens 999,998 doors at random and still hasn't revealed the car, despite the unliklihood of that happening, then the odds are still 50/50 that you have the right door. The odds at first might have been 1 in a million, but now they are 1 in 2 since the other 999,998 have been eliminated without a biased factor (Monty's choice).

It's the human element that always seems to get lost here. The real question is whether the other 999,998 doors are eliminated by someone who knows where the car is (Monty) or by chance.