there was someone who took a genuine interest in the basket. This person was Radha. Radha, the ordinary wife of an ordinary charioteer. Adhiratha, her husband, was a charioteer. He'd trained to be driving chariots for royals – at the moment though he was freelancing. Maybe if you were around in Ancient India you might have seen his advertisements posted here and there – Adhiratha's Chariot Service – with express service to all major ports, river banks, and temples.
The couple were childless. If Radha had been a Queen of Hastinapur, she would doubtless have been able to find a passing rishi to finagle some children out of them, directly or indirectly, as Kunti, Gandhari, and Satyavati had been able to. But being very poor, all they could do was to pray to the gods and hope for the best.
When Radha saw that the basket contained a baby, clearly unwanted by its mother, she dared to hope that this was an answer to her prayers. And when she realized that the baby was a boy, her patriarchal upbringing made her breathe a huge sigh of relief.
After that, Radha and Adhiratha rejoiced with their new baby boy. They tried tracing the origins of the baby of course but didn't get very far in their search before they decided to give up and focus on educating their new son instead.