Interesting point about probability theory being all slow. I don't think it's hard because it's all slow. There are many things that are all slow and I believe are easier. Programming, Physics, poetry. Granted "Thinking Fast And Slow" is on my reading list but I have read some overviews so please forgive where I'm jumping to conclusions with the book.

I feel the problem is exactly that probability calculation is not all slow. Our brains are geared to make probabilistic heuristics. And we make many of them and a lot of them are correct. The problem is not that it's slow like Newton's Laws of Motion. It's that in reality it is slow but a large fraction of the time our fast systems aren't bad at it. And so we struggle to shutdown our fast center.