They're both equally likely, because before you switch your door, a door that has nothing behind it is revealed.A door you didn't pick can get opened, a door you picked cannot.

A very simple way to consider the question:

If you keep your door, you win if and only if you pick the right door initially.

If you switch your door, you win if and only if you picked one of the two wrong doors initially.

Which case is more likely?

"A door you didn't pick can get opened, a door you picked cannot."

Right, and the other door I didn't pick can't get opened either.

I will look into what StoneTemplePython is saying because I need this answered mathematically: "why does the probability not change."