If you're interested in this stuff, I recommend Judea Pearl's Causality: Models, Reasoning, and Inference.

Basically, by using conditional probabilities you can in fact do the same math as CDT in situations that warrant it. Currently your math is a loosely-defined hodge-podge of what seem like it works, but if you look at Causality you'll see some sweet stuff.

Said sweet stuff still fails on cooperative or anthropic problems, though, so you do need something like UDT.