An interesting question

I enjoyed the discussion on skinny vs fat tyres in sand so much, I thought that I would pose another puzzle that I cam across recently. Not related to 4wding in any way but the answer is interesting.

You are a contestant on a games show and the host shows you three doors and asks you to choose one. Behind one of the doors is a million dollars, the other two have nothing.

Let's say you choose door number 1, the host then opens another door (call it door 2) to reveal that there is nothing behind it. He then asks if you want stay with your original choice (door 1) or change to door 3.

Do you:

a) Stay with your original choice (door 1)

b) Change to door 3, or

c) It doesn't matter which you choose.

Matt.