If p divided by q form gives defined result where q not equals 0 then why something divided by infinity is zero?

Usually, it's here that we're talking about a limit. So, it's not that something divided by infinity (which is not actually a number) is equal to 0, it's that as the limit as n approaches infinity, you'll get zero. So, take lim (n approaches infinity) of 1/n. You could plug some immensely large number in for n (say, 1,000,000,000 - which is getting large but not as big as infinity). If you divide 1 by this number, you're gonna get something so small, you could call it zero. So, it's not that we're dividing by infinity, we're approaching infinity - so plug some huge numbers in and see that you get really really close to zero.