Hey, I am currently learning about markov chains in my data management course, and I am stuck on a problem.

** Question: **
Three people - John, Joan and Kim - throw a ball

to each other. There is a probability of

that John will throw the ball to Joan.

There is a probability of

that Joan will throw the ball to Kim.

There is a probability of

that Kim will throw the ball to John.

a) Express this Markov chain as a transition matrix.

** Solution: **
Basically I am confused as to where to find the other probabilities. This is my transition matrix so far:

-----Joan-----Kim-----John

John-- 1/3-----------------

Joan-----------1/2---------

Kim---------------------1/4

(hopefully that turns out okay, I don't know how to do it using latex)

I know that each row is going to equal 1, so if I could find another probability in each row, I could finish the matrix. However, I do not know how to find the other probabilities.

Help, please!