# How is the probability transition matrix populated in the Markov process (chain) for a board game?

Following on from my other (answered) question:

With regards to the Markov process (chain), if an environment is a board game and its states are the various position the game pieces may be in, how would the transition probability matrix be initialised? How would it be (if it is?) updated?

Another example is estimating n-gram model: assume we want to train a model that will suggest a word in search field. We would analyze a corpus and calculate all 2 word sequences (for bigram model). Then, if a user starts typing I the model would suggest the word am, because I am occurs more frequently then I did, for example, and hence, the transition probability from I to am is greater.