When it is an adverb (modifying something), it means certainly, as in "я наверно придумаю что-нибудь плохое," which means "I will certainly come up with something bad."
When it is separated by punctuation, typically commas (or pauses in speech), it means probably. I would have written the answer as "Наверно, нет." For instance, take Okudzhava's Song About Combat Boots:
А где же наше мужество, солдат,
когда мы возвращаемся назад?
Его, наверно, женщины крадут,
и, как птенца, за пазуху кладут.
Of course, lots of confusion exists. For example, the Russian Wiki entry for the comedy The Gods Must Be Crazy is punctuated. But the meaning is almost the same.
I think the negation in your example is making the difference between the two loom large. Certainty, roughly speaking, is just probability going to one. An example of this is "almost sure/certain convergence" in math, which is translated as "почти наверное сходимость" in K. A. Borovkov's English-Russian Dictionary on Probability, Statistics, and Combinatorics, 1994.