I am currently trying to understand the probabilistic proof for hook-length formula for standard young tableaux of a given shape but at some step of the proof I am confused. I will attach a picture of the step in the proof where I got stuck since I don't see where the formula comes from and maybe somebody will be kind enough to help me with the explanation.
Thank you very much!
This is more of a comment than an answer. However, I'm too new a user to have comments enabled. In maths, it often happens that "simplifications" or "explanations" of proofs of great theorems are no clearer than the original versions. Therefore, I'd advise you to go to the original paper which this screen is explaining. The pdf is freely available if you simply google the authors. I have recently gone through the proof in the original paper myself, and was able to understand the proof fully. (I read only the proof, and not the Further Remarks section.) In my opinion, the proof does contain minor errors, but that is very much the norm. I would be happy to help you understand the original proof. After you've read it, please tell me if/where you're stuck, and I'll try to help.
Paul Epstein