Maximum value of negligible probability? We can see on many papers for cryptography that there are many uses of negligible probability to ensure something (security, correctness, etc).
How can we say that some probability is negligible?

I want to know the maximum value of negligible probability.
In other words, if we have a some probability $1/k$ for some $k$. 
What is the minimum $k$ that provides negligible probability?

Thank you.
It depends on context.

In a theoretical context, baring other definition, a probability is negligible if it decreases exponentially (or: faster than any polynomial of fixed degree) with some security parameter $k$, often a number of bits in the key; while the computational effort to use the system grows no faster than some polynomial of $k$.

In a practical context, if the probability is for one try of the adversary, and more tries will increase that probability about linearly, something like $2^{-80}$ used to be considered adequate, $2^{-128}$ is considered adequate for a decade or two baring hypothetical future quantum computers usable for cryptanalysis, $2^{-192}$ and $2^{-256}$ are sometime specified (because of security classification levels, and because that improves confidence when considering said quantum computers). Lower values will do, of course. Higher values (like $2^{-64}$) wight still make sense if the stakes are low and lowering that probability was costly, or forbidden by law.

In a practical context, if the probability is with all the parameters influencing it (effort of the adversary, number of users, size of plaintext..) set to credible values maximizing the probability, then $2^{-10}$ to $2^{-40}$ is reasonable, depending on how damaging the low-probability event would be. Lower values will do, of course.