Monty doesn't switch the door, the player does. You can imagine that if you are given a choice of three doors (1 with a car and 2 with goats), you have a 1/3 chance of guessing the door with the car on the first try. Therefore, the remaining 2 doors have a combined 2/3 chance of having the car. Now, Monty opens one of the remaining 2 doors with a goat (that is NOT the door you chose, nor the door with the car). Now, all of the sudden, since Monty has shown you one of the doors with the goat, the original 2/3 probability of the doors you didn't choose having the car gets "condensed" onto the door that you didn't pick. This is why choosing to switch doors will yield you 66% chance of winning, and choosing to keep your original door will yield you the original 1/3 chance of having chosen the correct door. Numberphile has a great video on Youtube that explains this problem.