Before the modern triumph of the definition of "subjective probability" associated with de Finetti (c. 1937), there were a multitude of attempts to formalize this vague concept. Here's John Maynard Keynes, from A Treatise on Probability (1921):

Probability is relative in a sense to the principles of human reason. The degree of probability, which it is rational for us to entertain, does not presume perfect logical insight, and is relative in part to the secondary propositions which we in fact know; and it is not dependent upon whether more perfect logical insight is or is not conceivable. It is the degree of probability to which those logical processes lead, of which our minds are capable; or, in the language of Chapter II, which those secondary propositions justify, which we in fact know. If we do not take this view of probability, if we do not limit in this way and make it, to this extent, relative to human powers, we are altogether adrift in the unknown; for we cannot ever know what degree of probability would be justified by the perception of logical relations which we are, and must always be, in capable of comprehending.