Assigning conditional probabilities to boolean functions

[bvssvni]

In the paper assigning probabilities to boolean functions I defined a transform from a boolean function constructed by a higher order if-function to the probability function of the boolean function returning true from independently randomized inputs.

I was wondering whether it is possible to assign conditional probabilities, ones that depend on the value of previous arguments. For example, if the first argument is A, its bias is P(A). The second argument B can have biases P(B | A) and P(B | ¬A).