Find the left eigenvector of the given stochastic matrix P that has eigenvalue 1. Normalize the vector so the sum of the entries is 1 (called a probability vector). The output vector should be a row vector.
(This can be thought of as a stationary distribution for a Markov chain. https://en.wikipedia.org/wiki/Markov_chain#Finite_state_space )
E.g: For P = [ .7 .3 ; .6 .4 ] return [ .6666666 .3333333 ] (or any vector close to this would be accepted).
The left eigenvector v of a matrix P (with eigenvalue 1) is a row vector such that v=v*P.