It doesn't really depend on the base rate though. The idea is that a high precision model will have all the targets at one end of the distribution, regardless of base rate.
Precision is P(T|R), where R is the event that a thing is reported, and T is the event that the thing is true. By Bayes' rule, P(T|R) = P(T)/(1+Pfa/Pd). So in terms of the traditional statistics Pd and Pfa, it is proportional to the base rate.