Author:LackiAbstract:It is unclear how frequently life and intelligence arise on planets. I consider a Bayesian prior for the probability P(ETI) that intelligence evolves at a suitable site, with weight distributed evenly over ln(1 - ln P(ETI)). This log log prior can handle a very wide range of P(ETI) values, from 1 to 10^(-10^122), while remaining responsive to evidence about extraterrestrial societies. It is motivated by our uncertainty in the number of conditions that must be fulfilled for intelligence to arise, and it is related to considerations of information, entropy, and state space dimensionality. After setting a lower limit to P(ETI) from the number of possible genome sequences, I calculate a Bayesian confidence of 18% that aliens exist within the observable Universe. With different assumptions about the minimum P(ETI) and the number of times intelligence can appear on a planet, this value falls between 1.4% and 47%. Overall, the prior leans towards our being isolated from extraterrestrial intelligences, but indicates that we should not be confident of this conclusion. I discuss the implications of the prior for the Search for Extraterrestrial Intelligence, concluding that searches for interstellar probes from nearby societies seem relatively effective. I also discuss the possibility of very small probabilities allowed by the prior for the origin of life and the Fermi Paradox, and note that similar priors might be constructed for interesting complex phenomena in general.