Learn Danish: Allergien kender lægen nok. - The allergy, the doctor probably knows.

This is called topicalization, which is the focus of this lesson. We put the direct object (Allergien) at the start of the sentence to emphasize it. Because Danish has a strict V2 (verb-second) rule, the verb (kender) must stay in the second position, which pushes the subject (lægen) into the third position.

How can we tell that lægen is the subject and not Allergien?

Grammatically, you cannot tell just by looking at the nouns! Both end in the definite article -en, and Danish nouns do not change their endings to show who is doing the action. You have to rely purely on context and common sense. Since an allergy cannot know anything, lægen (the doctor) must be the subject doing the knowing.

Why does this sentence use kender instead of ved for knows?

You use kender when you are familiar with a specific person, place, or thing (like an allergy). You use ved when you know a fact or a piece of information, which is usually followed by a clause or a pronoun.

I remember nok meaning enough. Why does it mean probably here?

You are right that nok often means enough, for example when talking about amounts. However, when it is used as a short adverb like it is here, it acts as a modal word that means probably, likely, or I suppose. It softens the sentence, showing that the speaker assumes the doctor is familiar with the allergy.