Markov Chains are really useful in a lot of fields. This problem will ask a question about a simple system with 3 states: A,B and C. The probability that one state will go to another can be given in a matrix such as:

mc = [0.5 0.2  0;
      0.2  0  0.6;
      0.3 0.8 0.4];

So, the first element is the probability that something in state A will remain in state A (0.5 here). The zero as the 5th element means nothing in state B will remain in state B. Now, if you are given the current state of the system, say state=[1 0 0], you can get the next state.

In this problem, I will given an incomplete matrix (A zero in place of one value), and then an initial state and the next state like:

states=[1 0.5;
        0 0.2;
        0 0.3]

You will have to provide the correct markov matrix as the output.