the probability of choosing the car the first time is 1/3.
the probability of choosing a goat the first time is 2/3.
If you chose a goat the first time, the probability of the host chooing the car is 1/2. So the probability of you choosing a goat and the result being counted is only 1/3.

So now you're in the situation where, if you chose the car the first time you will definitely win if you stick. But if you chose a goat the first time, you will definitely win if you swap. But the probability of each of those situations coming up is the same. i.e. 1/3, or 1/2 of the valid results.
( Moon Girl Technologies horrendous beanbag, Wed 27 Aug 2008, 11:54, archived)