1. Since $f(x)$ is an even function, its graph is symmetric with respect to the $y$-axis.
2. As $f(x) = f(2 - x)$ for any $x$, the graph is also symmetric with respect to the line $x = 1$.
3. Combining these two properties, $f(x)$ is a periodic function with a period of $2$.
4. Therefore, $f(20) = f(0)$.
5. Given that $f(x) = x - \frac{1}{2}$ for $x \in [0, 1]$, we can find $f(0)$ by substituting $x = 0$: $f(0) = -\frac{1}{2}$.
6. Thus, $f(20) = -\frac{1}{2}$.

The final answer is $\boxed{-\frac{1}{2}}$.