That's interesting, but that would be looking at it from the beginning, not on-the-spot chances.

At the beginning, you have a 1/3 chance of picking the right door, and a 2/3 chance of picking the wrong door.

Because there are three doors.

If you have one door picked, and the number of doors go down to two, you have a 1/2 chance. Period. It no longer matters how many doors there used to be. There are two doors, one of each, and you have a 50/50 shot of having chosen the correct one.

The switching makes sense when you explain it, but mathematically, it doesn't hold up.