Markov Chain probabilities

I have an example that is solved on one of the pages of wikipedia related to markov chains. I want to know how the probabilities (in bold) are calculated (please show the steps/formulas)


Another example is the dietary habits of a creature who eats only grapes, cheese or lettuce, and whose dietary habits conform to the following rules:

It eats exactly once a day.
If it ate cheese today, tomorrow it will eat lettuce or grapes with equal probability.
If it ate grapes today, tomorrow it will eat grapes with probability 1/10, cheese with probability 4/10 and lettuce with probability 5/10.
If it ate lettuce today, it will not eat lettuce again tomorrow but will eat grapes with probability 4/10 or cheese with probability 6/10.


TS Contributor
These are the transition probabilities of the Markov chain, and they are usually given like the parameters, but not the one the require you to solve. Usually you do the calculations based on this given matrix.

Of course in some problem you will need to write down the transition probabilities by yourself, which you may deduced by some specific hints in the problem. But not the case here.