This depends on how the host decides what door to open.
The 'always switch' answer depends on the fact the host will ALWAYS open a door with nothing behind it. If only one door has nothing then he must choose that one. If both have nothing he can toss a coin to decide.
In this case the original probability is 1/3 for each door. After he shows an empty door the probability drops to 0 for that one, 1/3 for your door and 2/3 for the other one.
My favorite way to view this is to offer a different choice. The host does not open any door. Instead he gives you the option to keep the one you have or trade for both the others. This is essentially the same deal as before.
The 'always switch' answer depends on the fact the host will ALWAYS open a door with nothing behind it. If only one door has nothing then he must choose that one. If both have nothing he can toss a coin to decide.
In this case the original probability is 1/3 for each door. After he shows an empty door the probability drops to 0 for that one, 1/3 for your door and 2/3 for the other one.
My favorite way to view this is to offer a different choice. The host does not open any door. Instead he gives you the option to keep the one you have or trade for both the others. This is essentially the same deal as before.