The observation can provide all sorts of information about the universe, including whether exploration occurs. The exact set of possible observations depends on the decision problem.

and can have any relationship, but the most interesting case is when one can infer from with certainty.

Good point. In that case the Drake equation must be modified to include panspermia probabilities and the variance in time-to-civilization among our sister lineages. I’m curious what kind of Bayesian update we get on those...