Think of p-value as the probability of an expected event to happen by chance and not because of your expectation or treatment. Indeed, if you have three independent events, the probability that all three to happen is the product of their probabilities.

However, there is a certain amount of approximation in computing the p-value. I don't know how you landed to the value of 0.001 in the first place, but it looks like you use a bootstrapping approach. If you did 10000 determinations, of which 10 appeared to be against your expectation, it doesn't mean that the p-value is 0.001. You need to identify the distribution of your variable, and based on how much your variable deviates from this distribution you can compute an accurate p-value.