In the preceding chapter, we have calculated the chances of an event, knowing the circumstances 
under which it is to happen or fail. We are now to place ourselves in an inverted position: we know the event,
and ask what is the probability which results from the event in favour of any set of circumstances under 
which the same might have happened.

De Morgan (1838), An Essay on Probabilities, Ch. 3 "On Inverse Probabilities"

Also:
† Fisher (1930), Math. Proc. Camb. Philos. Soc., 26, p 528, "Inverse probability", clearly distinguishes, perhaps for the first time, between Bayesian inference from flat "ignorance" priors ("the inverse argument proper"), the unexceptionable application of Bayes' Theorem when the prior describes aleatory probabilities ("not inverse probability strictly speaking"), & his fiducial argument.

‡ Pearson (1907), Phil. Mag., p365, "On the influence of past experience on future expectation", conflates Bayes' Theorem with the "equal distribution of ignorance".