@gpuccio here is a reference point for the discussion. This definition is from Hazen and Szostak.
I(Ex) = ?log2[F(Ex)], where F(Ex) is the fraction of all possible configurations of the system that possess a degree of function ? Ex. Functional information, which we illustrate with letter sequences, artificial life, and biopolymers, thus represents the probability that an arbitrary configuration of a system will achieve a specific function to a specified degree. In each case we observe evidence for several distinct solutions with different maximum degrees of function, features that lead to steps in plots of information versus degree of function.