There is quite a bit of literature on picking distributions in the absence of observations. "Probability Theory: The Logic Of Science" by E. T. Jaynes has a w

There is quite a bit of literature on picking distributions in the absence of observations. "Probability Theory: The Logic Of Science" by E. T. Jaynes has a whole chapter on "ignorance priors", where he shows how to pick prior distributions in the absence of quantitative information. Generally, these ignorance priors are improper (unnormalizable) distributions. One example is scale parameters, where the approriate prior is 'ds/s', which makes any order of magnitude equally probable. It doesn't have a mean, and it favors small values. A tiny bit of evidence will immediately turn it into a proper posterior distribution; I think this prior has zero information content. Of course, if one applies that approach to the Drake equation, one ends up with an equally uninformative posterior distribution, unless one can add evidence for each single variable. But that evidence just isn't there for some of them, so the result remains the same: It's impossible to estimate N, but it's probably very small. As it should be, given the total lack of data.