I like this 1,000,000 doors analogy.

Suppose there are 1,000,000 doors with a car behind one and goats behind the others. Select one! What is the probability the car is behind the one you selected? What is the probability the car is behind one of the other doors? You know that behind at least 999,998 of the other doors are goats. You know Monty knows where the car is. So now he opens 999,998 doors and you see all goats. Do you know any more than you did before he opened these doors? Has the probability that the car is behind your door changed? Has the probability that the car is behind one of the other doors changed? Do you want to switch?