Suppose that a density function is given by the formula $$f(x) = \begin{cases} {\frac{2}{95}} x & \text{if} \;\; 0 \leq x \leq 5\\ {\frac{1}{7}} - {\frac{1}{133}} x & \text{if} \;\; 5 \leq x \leq 19 \\ 0 & \text{otherwise.} \end{cases}$$ Find the probability that $x$ is between $4$ and $8$.