There are much more than 600 coins already
"A few years" is a short period of time. My guess is that no existing coins have a greater than 10% chance of passing Bitcoin in the next few years.
Ethereum is quite nice too.
Both of those aim to do something that bitcoin cannot do currently (but sidechains could potentially change this at least for some functions). I am a professional chess player. Many chess players have at least heard of bitcoin. I have yet to meet one who has ever mentioned Ethereum or Monero to me.
Most people still think money is the main purpose of blockchain technology. Ethereum wants to do a lot more but it will take a lot of continued development (years) before many of those applications are available for common users.
Monero addresses privacy concerns some have about blockchain technology. The general public still thinks bitcoin is anonymous by design. Once they realize that bitcoin has privacy issues will they suddenly want to switch? A very small percentage of the public uses a VPN or Tor. Privacy is important but I doubt enough people will agree that it is so important that a privacy focused coin will pass bitcoin in market cap within "a few years".
Change your timeframe from "a few years" to "5-10" years and I would reconsider my answer. Your 10% chance criteria sounds much more realistic over a slightly longer timeframe
Here is another question:
Do you think there is a greater than 10% chance the bitcointalk community will beat me in our current chess game? I have been pretty impressed with the quality of play by #teambitcoin so far
https://bitcointalksearch.org/topic/lets-play-a-game-of-chess-1148538