Markov Chains and rain statements

Question

Suppose that if it had rained for the past three days, then it will rain today with probability 0.8; if it didn’t rain for any of the past three days, then it will rain today w.p. 0.2; and in any other case, the weather today will be the same as the weather yesterday with probability 0.6. Determine P.

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I don't know how to get the matrix, please help me :c

Answer 1

Example to help you get started:

Let $D$ denotes that it doesn't rain and $R$ denotes that it rains.

For the row of $DRR$ and the column $RRD$, the corresponding value is $P(RRD|DRR)$, that is given that the past $3$ days is $DRR$, how likely is it that you will get $D$ on the very next day?

According to the descritption of the question, since it rains on two of the days, the probability that you get a $D$, an outcome that differs from the previous day is

$$P(RRD|DRR)=1-0.6=0.4$$

Also, note that a state's last two symbols must be the same as the first two symbols of the next state to have positive probability.