Suppose I put a prize in one of three boxes. You choose a box and then I must open one of the two boxes you did not choose to prove it is empty. Now, is the prize more likely to be in the box you originally chose or in the unopened box you didn't choose?
Answer: The prize is far more likely to be in the unopened box you did not choose. There is a one in three chance that you chose the box with the prize at the beginning. My showing you another box without it doesn't change those odds. Therefore there is a two out of three chance that the prize is in the unopened box you didn't choose.
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