One of my textbooks explains it this way:
ZNÁT -- to know, be acquainted with, be familiar with
VĚDĚT -- to know about, be aware of, be informed about
Helpful hints on when to use which verb (from the author of the textbook):
ZNÁT -- always takes a direct object
VĚDĚT -- usually followed by a clause
My own additional thinking on this:
"Vědět" also SEEMS to be used in the sense of "knowing" in general, that is, when there is neither a direct object nor a clause that follows it... just as in the sentence in this exercise.
"Czech: An Essential Grammar" by Naughton and "Grammar of Czech as a Foreign Language" are highly regarded and frequently recommended. The book I referred to in my comment is "Survival Czech" by Váchalová. Another that I've seen mentioned, though I haven't used it, is "Czech Step by Step." There may be references to others scattered throughout the discussions...
Because we have no object or subordinate clause I can only say because that is how we say it.
It may be helpful to consider the difference between these verbs in other languages as Czech is the typical language here and English is the exception with mixing both. German: wissen/kennen, French: savoir/connaître, Italian: sapere/conoscere. I do not know French or Italian, but in German it is "Wer weiß?" similar to Czech.