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You probably know about Monty Hall paradox. If not, you can read more about it at: http://en.wikipedia.org/wiki/Monty_Hall_problem
But if you do not feel happy with some probability calculation, you may want to see should we really change the door.
I wrote a small Python application to simulate Monty Hall problem.
You can access the program at:
http://www.codeskulptor.org/#user38_hxSeBAZW5H_1.py
You can see, after running 100 000 times, the change to win if you switch the door is approximately 2/3:
So now you can trust probability calculation.
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