Suppose your background assumption b and your regular probabilistic degree of belief function Pr are such that the hypothesis that all swans are white, x (S (x) W (x)), is independent of the claim that an arbitrary or "randomly chosen" object a is a swan, S (a):

Pr (S (a) | x (S (x) W (x)) b) = Pr (S (a) | b)

Suppose further that you are not certain what color a is given that it is a swan and,

in particular, that you are not certain that a is white given that it is a swan:

Pr (W (a) | S (a) b) < 1

Show that the claim that a is a white swan, S (a) W (a), incrementally confirms - in the sense of your regular probabilistic degree of belief function Pr - the hypothesis that all swans are white, x (S (x) W (x)) given your background assumption b. That is, show that the following holds:

Pr (x (S (x) W (x)) | S (a) W (a) b) > Pr (x (S (x) W (x)) | b)