If the integer $a$ is divisible by the integer $b$, which of the following notations correctly represents this relationship?

Step 1 (Definition of Divisibility): The statement '$a$ is divisible by $b$' means that $b$ divides $a$, meaning there exists some integer $k$ such that:

Step 2 (Identify notation): In number theory, the statement '$b$ divides $a$' is represented by the vertical bar symbol:

Step 3 (Avoid common confusion): The notation $a\mid b$ reads '$a$ divides $b$', which is the opposite statement ($b=a\cdot k$) and is not generally true when $a$ is divisible by $b$.

Step 4 (Conclusion): The correct notation is $b\mid a$, which is at option index 0.