Probability at its best!

Consider a function $f(x) = \begin{cases} \{ x \} + n , 2n \leq x < 2n + 1 \\ \lfloor x \rfloor - n , 2n + 1 \leq x < 2n + 2\end{cases}$ for integer $n$ .

A point $M = (x,y)$ is selected at random where $0\leq x \leq 6$ and $0 \leq y \leq f(x)$ .

If the perpendicular distance of $M$ from the $x$ -axis is smaller than its perpendicular distance from $f(x)$ , then the probability that $3\leq x \leq 4$ is given by $\dfrac2{a\left(3\sqrt b - 1\right)}$ , where $a$ and $b$ are positive integers.

Find the value of $|b-a|$ .