Columbus didn't have a picture of India's current map in his mind. To them India was where spices and other agricultural stuff came from. They had no particular race of people or civilization in mind.
Do realize that before the industrial revolution, wealthy were those who owned fertile land. 'India' as a concept was similar to 'Asia' to the eurocentric people - some eastern land with lush forests and fertile land. Which is why Indonesia came to be known as Dutch India and the Deccan Peninsula as British India - they really had no well-defined particular geographical region in mind.
Basically the colonial powers defined what constitutes India. Heck, even Burma was India!