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VAuroch comments on Dark Side Epistemology - Less Wrong
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The probability is the prior times the evidence ratio, so the higher the prior probability, the less evidence you need. If there's a lottery with one million numbers, and you have no evidence for anything, you'll think there's a 0.0001% chance of it getting 839772 exactly, a 50% chance of it getting 500000 or less, and a 99.9999% chance of it getting something other than 839772. Thus, you can be pretty sure it won't land on 839772 even without evidence.
Your knowledge of the rules of probability is evidence. It's not evidence specific to this question, but it is evidence for this question, among others.