Well, Monty doesn't know (or care about) your choice. He's 'constrained' by the fact that his 'probability' is 100%: he knows where the goats and car are.
You’re right. I forgot that you had to tell him which door you wanted to open (instead of just saying that you've decided on a door - like the FBI as just SAID that they've cracked the iPhone5). But it doesn’t matter because Monty was always going to open one of the two goat doors, and the one that he opens doesn’t matter to the 1/3 probability that you picked the car door. Your probability of getting the car ALWAYS doubles when you switch (even though you still may not get it).
If a has the car and b and c have goats, and you pick b, he opens c. And if you pick c, he opens b...