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One of the major goals for astronomy in the next decades is the remote searchfor biosignatures (i.e.\ the spectroscopic evidence of biological activity) inexoplanets. Here, we adopt a Bayesian statistical framework to discuss theimplications of such future searches, both in the case when life is detected,and when no definite evidence is found. We show that even a single detection ofbiosignatures in the vicinity of our stellar system, in a survey of similarsize to what will be obtainable in the next two decades, would affectsignificantly our prior belief on the frequency of life in the universe, evenstarting from a neutral or pessimistic stance. In particular, after suchdiscovery, an initially agnostic observer would be led to conclude that thereare more than $10^5$ inhabited planets in the galaxy with a probabilityexceeding $95$\%. However, this conclusion would be somewhat weakened by theviability of transfer of biological material over interstellar distances, as inpanspermia scenarios. Conversely, the lack of significant evidence ofbiosignatures would have little effect, leaving the assessment of the abundanceof life in the galaxy still largely undetermined.

Quantifying the information impact of future searches for exoplanetary biosignatures