$k$ defects are randomly distributed amongst $n$ integrated-circuit chips produced by a factory (any number of defects may be found on a chip and each defect is independent of the other defects).

Let $p(k, n)$ represent the probability that there is a chip with at least $3$ defects.
For instance $p(3,7) \approx 0.0204081633$.

Find $p(20\,000, 1\,000\,000)$ and give your answer rounded to $10$ decimal places in the form 0.abcdefghij.