$p$ is a finite Markov chain where $p(i,j)>0$ for all $i,j$. Prove a reversible stationary distribution exists for $p$ if
$p(i,j)p(j,k)p(k,i)=p(i,k)p(k,j)p(j,i)$ for all $i,j,k$
This question is from Durrett's Essentials of Stochastic Processes. There is a hint provided that says: Hint: fix $i$ and take $π_j = cp(i,j)/p(j,i)$ where $c$ is some constant.
I am struggling to see how to apply this hint. I want to show $c$ is $π_i$ but don't know how to get there.