"There is no fire here."
Translation:Itt nincs tűz.
Not really, no. It's "is not", if anything, and not "not a(n)". Do all Hungarian sentences with "nincs" have a German equivalent with "kein"? It's possible but I wouldn't say for sure. Do all German sentences with "kein" have a Hungarian equivalent with "nincs"? Not at all. Ich esse keinen Apfel - Nem eszek almát. / Nem eszek egy almát sem. ("I don't eat apple", "I don't eat not even one apple")
So, at the end of the day, "kein" is like a negative indefinite article, "nincs" is the negative counterpart of "van".