[dfxm12]

Maybe this will help understand it intuitively. You have a choice between doors 1 2 3. You pick door 1. You know the odds of the car being in door 1 is 1/3. The odds of the car being in door 2 or door 3 are 2/3.

Monty opens door 3, showing a zonk. You knew there was a 2/3 chance of the car being in door 2 or 3, but now you know there's a 2/3 chance of the car being in door 2 (since you know it is not in door 3).

All this didn't change anything you know about door 1. It has the same 1/3 chance it started with. Probability is all about what you know in the moment.

The math involves understanding the rules, that Monty will never open the door you picked and will never open the door with the car behind it. This is why one can't look above and say "well, there is a 1/2 chance of the car being behind door 1 after door 3 was opened and there wasn't a car there". This would only be true mathematically if the door Monty opened was random, but we know the door Monty picks isn't random. In fact, the pool of doors that could be opened depends on your initial pick. Monty was never going to open door 1 (the door that you picked), even if it was a zonk & Monty was never going to open the door with the car, therefore one can't make that assertion.