Here's a thought experiment. You're going to use a Star Trek teleporter-like device to make an exact copy of yourself. What are the odds that you end up being the copy? Or rather, what should you believe the odds are that you will be the copy?
Of course, I, the original, will not be the copy, but if I go in knowing I'm not the copy, the the copy will come out knowing he's not the copy. Thus, you should go in believing there's a 50% chance you are the copy, and then both the original and the copy will come out with a logically consistent belief.
A good way to know for sure would be to use a sharpie to draw a mark on the inside of the particular chamber you step into before the machine is activated. Then, after you are copied, both people will have the memory of drawing such a mark. But the copy, who just materialized in a second chamber, will be surprised to find that there is no mark in front of him.
Of course, I, the original, will not be the copy, but if I go in knowing I'm not the copy, the the copy will come out knowing he's not the copy. Thus, you should go in believing there's a 50% chance you are the copy, and then both the original and the copy will come out with a logically consistent belief.