Damn. Impressed to see something this fundamental that never made it into my computer science postgrad education (and judging by the depths and difficulty of it, might not for a while!) Seems like a powerful technique that scales to cover quite a lot of other problems.
Wow I'm really surprised this didn't enter your post grad! We covered this briefly in undergrad but had a much meatier grad level course on fundamentals of computational with this included and it destroyed pretty much every student in the class lol. Our professor ended the final at 4 hours to "spare you the misery".
hahaha okay actually in retrospect/closer inspection, I do think some teachers tried to instill these probability proofs from a different angle - though obviously it did not stick long past the testing, and I never thought of it as a fundamental new approach. Would definitely need to reformulate all of this into much more intuitive / visual metaphors to get it to really stick these days. Oddly I do a lot of thinking on the general fundamentals course content these days (FSAs, Turing Machines, etc) but I should really try to incorporate this probabilistic view