Answer
The probabilities are identical.
Work Step by Step
The probability density for each particle is the square of its absolute value, equal to the product of $\Psi(x,y,z,t)$ and its complex conjugate, $\Psi^*(x,y,z,t)$.
For particle A, we obtain $|\Psi(x,y,z)|^2$.
For particle B, we obtain $|\Psi(x,y,z)|^2e^{i \phi} e^{-i \phi}=|\Psi(x,y,z)|^2$.
The probability distribution functions for the particles are identical, and so the probabilities described are too.
