Failing probability

I find this annoying.

Everyone on the "switch" side continues to assert that Monty's pick of the two doors you didn't choose somehow magically alters the probability of the remaining door you didn't choose being correct. But I can't see as that's possible.

Door 1: Goat
Door 2: Car
Door 3: Goat

I choose door 1. I'm getting a goat if I don't switch. Monty opens door three, revealing the second goat. Switchers say I now know something about door 2, but that's not the case. Door 2 could just as easily contain a goat, with me sitting on the car. Monty's revelation doesn't change anything, except that I now have a fifty-fifty chance of being right. The same chance I have had all along, because I know that no matter what door I pick, Monty is going to open one of the two goat doors. Saying that you magically get a transference of probability to one door or the other on the basis of his pick makes no sense to me.

Argh. Stuff like this probably explains why it took me two semesters to pass freshman calculus.