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TheOtherDave comments on What Bayesianism taught me - Less Wrong
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Well, you'd do better to search all of those volumes at once. Doing it one volume at a time has a significant chance of failing to find the moons even if they exist, since the moons move over time, and therefore failing to find them isn't significant evidence of their nonexistence.
But that's largely orthogonal to your point.
Kinda hard to do, but more to the point, the assumption that a single search is sufficient (= nothing changes with time) may not be true.
In fact, if you want to update your beliefs with absence of evidence, then every time your glance sweeps across a volume of space which physically could hold a tiger you need to update your beliefs about non-existence of tigers.
And then you get into more trouble because if your beliefs in (non)existence of tigers are time-specific, as they should be, the evidence from the previous second might not be relevant to the (non)existence of tigers in the next second. You need specific assumptions about persistence of entities like tigers on certain time scales (e.g. tigers don't persist on the time scale where the unit of time is a billion years).
(nods) Systems that don't assign very low priors to such "evasive" events can easily wind up incorrigibly believing falsehoods, even if they process evidence properly.