I'm wondering where the relative probabilistic distance was first studied: $$d(A,B) =\mathbb P(\overline A\cup\overline B\mid A\cup B)$$ where $\overline A$ is the complement of $A$.

A web search turned up this:

Goodman, I. R. and Kramer, G. F. (1996), Extension of relational event algebra to a general decision making setting, Proceedings of the Conference on Intelligent Systems: A Semiotic Perspective, National Institute of Standards and Technology.

where $d$ is called $\mathbf r_{\mathbb P}$, but surely that's not the first occurrence?