More about investment (Money/time training) than population.
I don’t really think its about money; Indian institutions are able to spend far more on sports than most African/Asian /and even South American countries.
It’s more a question of cultural priorities; physical sports are rarely considered as a means of livelihood.
Nearly all “talented” sportspersons in India, who are identified at school level, aim to enter college under the sports quota. From there, the aim is primarily to get into government-run companies such as Air India or the Railways, which also hire under a sports quota. So, once you have a cushy 9-5 job where you get to live your sports passion by playing and winning domestic events, why stress yourself for something like the Olympics?
Two of India’s last individual medals were in shooting: one was won by a guy from a very rich family while the other shooter was an army officer: neither depended on the classical state system that I described above.