Wiener made important contributions to mathematics but not to information theory. He wrote a book saying that entropy is related to "information" and is maximized for a Gaussian. That's about his involvement. The paper attached goes way beyond that.
This "surprisal" can be parametrized by relative entropy (Kullback-Liebler divergence), which reduces to the Shannon entropy formula only when the observer has the correct anticipated distribution.
> With Shannon’s startling ideas on information, it was one of the rare moments in history, an academic would later point out, “where somebody founded a field, stated all the major results, and proved most of them all pretty much at once.”
It is attributed to a documentary on Claude Shannon: https://www.youtube.com/watch?v=z2Whj_nL-x8