Let $E$ be “the choosing of a number on the interval $[0, 1]$ such that the
number is less than $1/3$. In this case, the use of the definition is a bit more
subtle but essentially it gives

$$\mathbb P(E)= \dfrac{\text{Length of } [0, 1/3)}{\text{Length of }[0,1]}$$

Here is the image of the interval:

[![enter image description here](https://i.stack.imgur.com/5IqmB.png)](https://i.stack.imgur.com/5IqmB.png)