The introductory section of Thomas Bayes's famous essay on probability contains two arguments for what we now call the rule of conditioning. The first argument, which leads to Bayes's third proposition, can be made rigorous if we use rooted trees to represent the step-by-step determination of events. The second argument, which leads to Bayes's fifth proposition, does not stand up to scrutiny.
"Bayes's Two Arguments for The Rule of Conditioning." Ann. Statist. 10 (4) 1075 - 1089, December, 1982. https://doi.org/10.1214/aos/1176345974