There is North Agalega, an island controlled by Mauritius, India's long-standing ally.
This is where India is building its base.
It might seem like the middle of nowhere, but look around and it will make perfect sense.
To the south is the Reunion island, controlled by the French, another close ally, and to the north is Djibouti, China's foothold in Africa where they have a military base.
So the Indian base serves two objectives.
The first is to coordinate with allies and in fact, this is already happening as India recently conducted joint patrols with French vessels from the Reunion.