Consider the following example:

1) The starting point is A

2)The probability to go from A to B is 3/5

3)The probability to go from A to C is 1/5

4)The probability to stay at A is 1/5

5)If you are at B you can never return to A

6)There is no direct way from B to C

7) There is an infinite number attempts to reach C

What is the probability of ever reaching point C?

i would suggest its 4/15, what do you think?