Let's say we have 60 balls of which 17 are red and the rest black. If I pick 7 balls at random, what is the probability that i picked at least 3 red balls?

Evidently, yes, and my action is based on experience on many forums. See Bayes' Theorem and the Reasonable Person standard.

Since you now have at least two search results by two different people (yourself & me) are you in any better shape to understand the question and answer it?