Theory due especially to English economist John Maynard Keynes (1883-1946) in his Treatise on Probability (1921), Chapter 1.
It says that the probability of a hypothesis is a logical relation (rather like logical entailment, only weaker) between a hypothesis and a body of evidence for it. Probability is thus made relative to evidence.
This could be avoided by considering all the evidence (requirement of total evidence), but there are difficulties in specifying this.
The relation in question is hard to specify, and would not give an analysis of 'probably' anyway, for if we have some evidence which entails a conclusion we can assert the conclusion; but if it only makes it probable ('probabilifies' it) we can only say 'the conclusion is probable', without saying what this means (unless we are saying merely that the evidence exists, without saying what it does, that is without using it).
The theory is also subject to various paradoxes.
H E Kyburg, Probability and Inductive Logic (1970), ch. 5