Bill, have a look at the notes for this chapter: https://www.duolingo.com/skill/la/places/tips-and-notes

Num The particle num indicates that the speaker expects a negative answer; the speaker would be surprised if someone answered yes.

I suppose in this case the 'surely' is a fixed negative. Hope someone can eloborate on this!!

It's not surely, it's "surely not" = num.

Word by word: "Surely not" Corinna lives alone.

(Then, we have to change the word order in English, to agree with the English grammar order.)