In an iḍāfah construction, the first noun is annexed to the second. In suitable constructions this relation can make a previously indefinite subject definite.
Examples:
«غُلَامٌ» — a servant, without an identifying relationship.
«غُلَامُ زَيْدٍ» — Zayd's servant.
«غُلَامِي» — my servant.
«جَاءَ غُلَامِي» — My servant came.
Here the relation to the speaker helps identify the servant. Yet not every annexation creates definiteness, and definiteness does not necessarily prove that only one such servant exists. Context may still disambiguate the intended person.
We should distinguish grammatical definiteness from complete practical identification.