Functional equation with three variables

I have a functional equation with three variables. $f(x,y,z)$ is a real function with three variables where y is different from z i.e., $f(x,y,z)$ defined only for $y \neq z$. This function satisfies

1. $f(x,x,y)=0$


2. $f(x,y,x)=1$


3. $f(x,y,z)f(z,y,r)=f(x,y,r)$

What is the general solution for $f$?