Conditional probability when both sets measure zero Suppose I have a sample space $\Omega = [0, 1] \subset \mathbb{R}$, and I have two events $A = \{0, 1/4, 1/2, 3/4, 1\}$ and $B = \{0, 1/2, 1\}$.
Then it seems clear that $P(B | A) = 3/5$.
The rule I have seen for computing conditional probability is $P(B|A) = P(B \cap A)/P(A)$ when $P(A) \neq 0$.
However, in my case $P(A) = 0$. I am able to compute the conditional probability by approaching from a different direction.
Is there a general rule on how to compute these conditional probabilities?

You can use $P(A|B)=\dfrac{P(A\cap B)}{P(B)}$ only when $P(B)>0$. If $P(B)\neq0$ then $P(A|B)$ is given "any" arbitrary value, but just to be clean, define $P(A|B)=0$.
By the way, in your given example, I do not understand one crucial thing: what is your probability measure?
