[stordoff]

In your reverse problem, I don't see how the new door can ever be relevant, as you know the car is behind 1 or 2, so you're only ever interested in picking between those 2.

In the original problem, its presence _is_ relevant, as the car could be behind doors 1, 2, or 3. Say you pick door 1 - there's a 1/3 chance you are right.

The host is then left with doors 2 and 3. We know there is a 2/3 chance the car is behind _one_ of these doors. When the presenter reveals a goat (say in door 2), he is reveling information about this set of doors - there is still a 2/3 chance that the car is behind one of the doors in this set, but there's only one door left we don't know anything about (3). There is therefore a 2/3 chance that it is behind _this_ door.