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Lumifer comments on Open Thread, Apr. 20 - Apr. 26, 2015 - Less Wrong
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You want to figure out whether to do as the oracle asks or not. To do this, you would like to predict what will happen in each case. But you have no evidence concerning the case where you don't do as it asks, because so far everyone has obliged. So, e.g., Pr(something good happens | decline oracle's request) has Pr(decline oracle's request) in the denominator, and that's zero.
That's a forward-looking probability and is certainly not zero.
In the absence of evidence you just fall back on your prior.
In order to get Error: Divide By Zero, you have to be using a particular kind of decision theory and assume P(decline oracle's request) = 0.
Your prior for what?
For the baseline, "underlying" probability of the oracle's request being declined. Roughly speaking, if you have never seen X happen, it does not mean that X will never happen (=has a probability of zero).
This assumes you're a passive observer, by the way -- if you are actively making a decision whether to accept or decline the request you can't apply Bayesian probabilities to your own actions.