The probability of an event, $P(A)$, is a definite number.
I can espress $P(A)$ as $P(A)=p(a)da$ where $p(a)$ is the probability density function.
However, $da$ is NOT a definite value, so how it's possible to get a definite quantity calculating $p(a)da$ and ascertain that effectively $P(A)=p(a)da$ ?