Interesting stat class question

This question was brought up during class the other day. Wondered if there's a solution and how it's figured.

On an old game show, the final contest involved 3 doors. One had a prize behind it, the other two had nothing. You could pick one door, and before it was opened the host would take away one wrong door of the two other possible doors. You then had the option of staying with the door you picked or taking the other one. The question was should you keep the door you originaly picked or switch, why, and would the probability of getting the right door be affected?