  Typically, when estimating the prior transit probability, one assumes a
uniform distribution for the cosine of the inclination angle i of the
companion's orbit, which yields the familiar estimate of ~R_*/a. However, the
posterior transit probability depends not only on the prior probability
distribution of i but also on the prior probability distribution of the
companion mass M_c. In general, the posterior can be larger or smaller than the
prior transit probability. We derive analytic expressions for the posterior
transit probability assuming a power-law form for the distribution of true
masses with exponent alpha. For low transit probabilities, these probabilities
reduce to a constant multiplicative factor of the corresponding prior transit
probability. The prior and posterior probabilities are equal for alpha = -1,
whereas the posterior transit probability is ~1.5 times larger and ~4/pi larger
for for alpha = -3 and alpha = -2, but is less than the prior for alpha >= 0,
and can be arbitrarily small for alpha > 1. We also calculate the posterior
transit probability in different mass regimes for two physically-motivated mass
distributions of companions around Sun-like stars, finding that the posterior
is likely higher for Super-Earths, Neptunes and Super-Jupiters. We therefore
suggest that companions with minimum masses in these regimes might be
better-than-expected targets for transit follow-up, and we identify promising
targets from RV-detected planets in the literature.
