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http://robotics.eecs.berkeley.edu/~wlr/126/w12.htm

when you draw this graph how can you sure that state go from 1 to 2 is 100%?

look at first example, there is a p and q is it probability from 1 to 2 that is drawn only when P(from 1 to 2) > 0.5, such as p = 0.8?

look at example For [6], d(1) = g.c.d.{3, 5, 6, ..} = 1 1 -> 2 -> 3 -> 1, then there is 3, will above consideration change this calculation? what is the relationship between using this p and q and gcd?

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On the first chain

g1

the transition probability from 1 to 2 is found next to the arrow pointing from 1 to 2. This probability is denoted by $b$. If $b<1$, the probability of going from 1 to 2 is less than 100%.

On the 5th and 6th chains

chain6

the only arrow leaving 1 is the arrow toward 2. Although probabilities are not specified, the absence of arrows from 1 to 1, 3 or 4 means that the corresponding transitions have probability zero. The probability of going from 1 to 2 is equal to $1$ (or 100% if you prefer).

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