a/an just means 'one of a class' the means 'you know exactly which one'.
Compare:
A doctor must like people. ( = any doctor, any one of that profession) My brother's a doctor. ( = one of that profession) I'm going to see the doctor. ( = you know which one: my doctor) I live in a small flat at the top of an old house near the town hall. (a small flat: there might be two or three at the top of the house — it could be any one of these. an old house: there are lots near the town hall — it could be any one. the top: we know which top: it's the top of the house where the person lives — a house only has one top. the town hall: we know exactly which town hall is meant: there's only one in the town.)