Basic stats research question

Say that I have two collections of data. The first is a background collection, where I gather two sets of features f1_b: N1xd1, and f2_b: N1xd2.

During the second collection of data I get f1_n: N2xd1 and f2_n: N2xd2.

Basically I want to know how probable f1_n and f2_n are given the background data. Is there a good way to go about doing this? So something like P(f1_n, f2_n | f1_b, f2_b).