Hum, I've often pondered what probability actually means for quantum mechanics—that is in respect of its actual underlying mechanics. The more I think about it the more I agree with Sir Roger Penrose: https://www.youtube.com/watch?v=sGm505TFMbU (40:36 - 46:36. One should however view the whole video for proper context.)
This story on probability just further firms up my view.