Markov Model transition probability

Markov Model transition probability

Hy, i have a little doubt about a Markov model problem. The problem
requests to find a transition probability matrix for a situation with two
statistically indipendent person that can be in 4 different state S1, S2,
S3, S4. The transaction probability for one person is:
state 1 goes directly back to state 1 with probability 0.4 and to state 2
with probability 0.6. State 2 goes directly to states 1 or 4 with
probabilities 0.2 and 0.8, respectively. State 3 goes directly to states
1, 3, or 4 with probabilities 0.1, 0.7, and 0.2, respectively. State 4
goes directly to states 1, 3, or 4 with probabilities 0.3, 0.2, and 0.5,
respectively.
I've constructed the model with the notation (X,Y,Z,W) finding 16
different states. For example state (AB,0,0,0) indicate the two person in
the state S1. (A,B,0,0) indicate the person A in S1 and person B in S2 and
so on. Enumerated the states i have to find the transition probability
but, wath is the transition probability from state (AB,0,0,0) to
(A,B,0,0)? Haw can i find it having only that for one person?
Bye