Does absence of evidence equal evidence of absence? I hear atheists spout this claim ad nauseam, and I'd like to post a hopefully helpful explanation to why such a claim doesn't logically follow.

Imagine there exists a planet around a distant star but we have no evidence it exists, no one has observed it, but no one has checked the star to see if a planet is orbiting it. In this case, we have no evidence that such a planet exists, but is such a planet improbable? Not at all, given the lack of information we have about the star we are forced to make the neutral claim that the probability of a planet orbiting that star is 50%. But, if we analyze the star and find no evidence such as the star shifting position due to the gravitational pull of the planet, then we can say it is improbable that such a planet exists. Why? Because there was no evidence, where there should have been. This is an elementary point in logic, that no logician or philosopher denies, so why so many atheists can't seem to understand it is beyond me.