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Manfred comments on Logical uncertainty, kind of. A proposal, at least. - Less Wrong
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I agree with the rest of your comment, but this seems too ad hoc. It runs into trouble if outcomes differ in utility, so that you can't just look for high probability. And storing a number seems like a much better way of integrating lots of independent pieces of information than storing a list.
Then you look for largest probability*utility , which you generally do by trying to find a way to demonstrate A>B which you can do in many cases where you can't actually evaluate either A or B (and many cases where you can only evaluate A and B so inaccurately that outcome of comparison of evaluations of A and B is primarily dependent on inaccuracies).
Furthermore, a "probability" is a list due to loss of statistical independence with other variables. edit: the pieces of information are very rarely independent, too. Some reasoning that 3 is more likely than other digits would not be independent from 2 being a bad choice.
edit: also, holy hell, trillionth prime does end with 3.