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Desrtopa comments on A Voting Puzzle, Some Political Science, and a Nerd Failure Mode - Less Wrong
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Quite a lot of people assign "certainty" to things which later turn out not to be true. Quite often they "check," but they either check wrong, or they make mistaken inferences from their observations which they do not realize they should doubt.
The fact that we haven't looked for Russell's Teapot actually makes very little difference with respect to what we should estimate for its probability. A strong prior is a strong prior.
Are you sure this is a strong prior? Strong priors are relatively unmoved by evidence and evidence of a teapot in orbit would probably demolish that prior fairly thoroughly :-)
Not to mention that there is the whole issue of how that prior came to be. Standard Bayesian reasoning conveniently assumes that priors spring out fully-formed ex nihilo but that's not a very satisfying approach.
Strong priors take strong evidence to move them appreciably, but physically going out and finding a teapot would be very strong evidence of a teapot.
On the other hand, if an astronomer using an extremely powerful telescope claimed to find one, then unless you subsequently received serious corroboration, you'd be wiser not to believe it, because the strength of the prior is such that it's more likely that they're simply lying or mistaken.
Your prior in any situation is your best estimate given the information available to you before consolidating some new piece of information, so a prior can in fact be based on extensive observation.