Because "the police" is a collective noun in English. It stands for a group of people (the entire police force) and therefore it needs a plural verb, "show". However, if it was a single police officer who showed her the way, it would of course be singular and "shows".
But, I'm not a native English speaker, so I could be wrong.
I think treating collective nouns as plural is more prominent in British English than American English (which Duo presumably uses) though