These arguments are all off the mark. There is no "harder" involved. It's a pure numbers game, and as such a dollars and cents game.
A "professional" league is professional league due to the willingness of the fans to pay to see you play. The greater the demand to watch the sport, the more money given to the players to distribute, and given enough demand, a league can expand, thus increasing the number of professional players.
So, to find out the "chances" of making a pro sport, you have to find out the approximate number of total participants of that sport, adjust for the top X percent who are skilled enough to get the chance to put the requisite practice time in to give them a realistic chance (Malcolm Gladwell says that this is 10,000 hours), vs the number of pro spots available.
You could further argue that the number of dollars available to distribute to the athletes adjusts the number of bottom level participants. A good case study of this would be MMA. 15 years ago, you could have become a "Pro" at this, just by being in shape, and being a little crazy. Now, with the amount of money available to the top performers, there are lot more athletes aspiring to be a "Pro".
I don't have the time to figure this out, but I'm sure with a little work, someone could easily figure out the probability of becoming a "Pro" in each major sport.