[indigodaddy]

Odds aren't changing at any point. It's as simple as you were initially sitting in a 1/3 "probability block" (the way I like to think of it)... ; and then you shifted over to a 2/3 "probability block."

When or where are any odds changing?

[ColinWright]

The probability on the two you didn't open is 2/3. At that point you have no information as to which of those two doors holds the prize, so they each have probability of 1/3.

Then the host opens one. The probability of the door opened holding the prize goes to 0. But the probability on the set of two is still 2/3, and so the probability of the door that is both unchosen and unopened goes to 2/3.