Russell says in the ‘Problems of Philosophy’:
It must be known to us that the existence of some one sort of a thing, A, is a sign of the existence of some other sort of thing, B, either at the same time as A or at some earlier or later time, as, for example, thunder is a sign of the earlier existence of lightning. If this were not know to us, we could never extend our knowledge beyond the sphere of our private experience;
Expectations of uniformity of experience seems inherent to human and animals. The question is
Do any number of cases of a law being fulfilled in the past afford evidence that it will be fulfilled in the future?
Russell says we can only say what is probable, or likely to happen. This must be good enough, rather than pure chance is there some reasoning for favouring that they will.
Provided we concede that two things found together and never apart can not be said to persist this way in all futures, we merely state that the more cases they are together through time the more probable they’re association is.
Russells principle of induction is a way to make claims about future events:
The greater the number of cases in which a thing the sort A has been found associated with a thing the sort B, the more probable it is (if no cases of failure of association are known) that A is always associated with B;
Under the same circumstances, a sufficient number of cases of the association of A with B will make it nearly certain that A is always associated with B, and will make this general law approach certainty without limit
Russell says probability is always relative to a set of data, in this case, the set of A’s and B’s observed. The probability assigned to some relationship is not ‘disproved’ by a counter example, that counter example updates the probability.
The above could also be the creative context of probability.