The probability of seeing a vertex $v_j$ in less than $K$ steps from another vertex $v_i$

Question

I want to calculate the probability of seeing vertex $v_j$ in a random walk in less than $K$ steps from vertex $v_i$ for every pair of vertices. Is there any approach for this problem in polynomial time? Actually I want to calculate the $p(v_j|v_i)$ in a window of width $K$, but my problem is that there might be more than one path from $v_i$ to $v_j$.