I think Einstein would've considered nonlocal hidden variables the same as spooky action at a distance. >How is that probability distribution different from a

I think Einstein would've considered nonlocal hidden variables the same as spooky action at a distance. >How is that probability distribution different from a hidden variables, except that it's not a straight number but a function instead? Because for entangled particles (separated by a large distance! but also any entangled particle) their PDFs will be correlated in a way that is impossible to define for just a single particle. This makes physicists uncomfortable because of relativity and things happening faster than light.