  One of the major goals for astronomy in the next decades is the remote search
for biosignatures (i.e.\ the spectroscopic evidence of biological activity) in
exoplanets. Here, we adopt a Bayesian statistical framework to discuss the
implications 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 of
biosignatures in the vicinity of our stellar system, in a survey of similar
size to what will be obtainable in the next two decades, would affect
significantly our prior belief on the frequency of life in the universe, even
starting from a neutral or pessimistic stance. In particular, after such
discovery, an initially agnostic observer would be led to conclude that there
are more than $10^5$ inhabited planets in the galaxy with a probability
exceeding $95$\%. However, this conclusion would be somewhat weakened by the
viability of transfer of biological material over interstellar distances, as in
panspermia scenarios. Conversely, the lack of significant evidence of
biosignatures would have little effect, leaving the assessment of the abundance
of life in the galaxy still largely undetermined.
