stuck on island (probability) There are many islands that are connected by one-way bridges, that is, if a bridge connects islands a and b , then you can only use the bridge to go from a to b but you cannot travel back by using the same. If you are on island a , then you select (uniformly and randomly) one of the islands that are directly reachable from a through the one-way bridge and move to that island. You are stuck on an island if you cannot move any further. It is guaranteed that after leaving any island it is not possible to come back to that island.
Find the island that you are most likely to get stuck on
What I have tried:
suppose I am going from 3 to 4  then probability of getting stuck on 4 = probability of stucking at 3 /no of ways getting out of 3
if it is correct then what we call the above method like i know about conditional probability .
If not then what should be the correct method?
Problem link Island
 A: There is more than one approach to this question.  The following, based on Markov chains,  works but may not be the most efficient when you have hundreds of thousands of islands
Taking the example from your link (five islands where you starting at island $1$, and there are bridges from island $1$ to $2,3,4$, from island $2$ to $4,5$, and from island $3$ to $4$), you can find the probability of your island after $n$ moves or attempted moves as 
$$\begin{bmatrix} 1& 0 & 0 & 0 & 0 \end{bmatrix} \begin{bmatrix}
0 & \frac14 & \frac14 & \frac14 & \frac14  \\
0 & 0 & 0 & \frac12 & \frac12  \\
0 & 0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1 & 0 \\
0 & 0 & 0 & 0 & 1
\end{bmatrix}^n$$
so 


*

*with $n=0$ you start at island $1$, i.e. $\begin{bmatrix}1& 0 & 0 & 0 & 0\end{bmatrix}$

*with $n=1$ the distribution of where you may be is $\begin{bmatrix}0 & \frac14 & \frac14 & \frac14 & \frac14\end{bmatrix}$

*with $n\ge 2$ the distribution of where you may be is $\begin{bmatrix}0 & 0 & 0 & \frac58 & \frac38\end{bmatrix}$
In this example you can conclude that you will get stuck on one of islands $4$ or $5$ after two or fewer moves, with island $4$ being more likely
In general, if given no possibility of returning to an earlier island, then the number of moves until you are stuck must be less than the number of islands, so this is a finite algorithm  
