  The probability that life spontaneously emerges in a suitable environment
(abiogenesis) is one of the major unknowns in astrobiology. Assessing its value
is impeded by the lack of an accepted theory for the origin of life, and is
further complicated by the existence of selection biases. Appealing
uncritically to some version of the ``Principle of Mediocrity'' -- namely, the
supposed typicality of what transpired on Earth -- is problematic on empirical
or logical grounds. In this paper, we adopt a Bayesian statistical approach to
put on rigorous footing the inference of lower bounds for the probability of
abiogenesis, based on current and future evidence. We demonstrate that the
single datum that life has appeared at least once on Earth merely sets weak
constraints on the minimal probability of abiogenesis. In fact, the {\it a
priori} probability assigned to this event (viz., optimistic, pessimistic or
agnostic prior) exerts the strongest influence on the final result. We also
show that the existence of a large number of habitable worlds does not
necessarily imply, by itself, a high probability that life should be common in
the universe. Instead, as delineated before, the choice of prior, which is
subject to uncertainty (i.e., admits multiple scenarios), strongly influences
the likelihood of life being common. If habitable worlds are uncommon, for an
agnostic prior, a deterministic scenario for the origin of life might be
favoured over one where abiogenesis is a fluke event.

Earth and Planetary Astrophysics;Instrumentation and Methods for Astrophysics;Populations and Evolution