It is a common saying that markov-chain is a special case of probability course. That is to say, It means an unchangeable markov-chain process of the transition-probability of discontinuous time. There are two kinds of ways to show transition probability parade matrix theory. The first is the way by arrangement of a rightangled tetragon. The second part is a vertical measurement and direction sing by transition-circle. In this essay, I try to find out existence of procession for transition-probability applied markov-chain. And it is possible for me to know not only, what it is basic on a study of chain but also being applied to abnormal problems following a flow change and statistic facts expecting to use as a model of air expansion in physics.