How many professional cyclists are there in the world?

The number varies. On a contemporary Pro Tour team there could be as many as 29 cyclists in total under contract at a given time. No race ever requires that many riders on a team, so team members ride in various races, often at the same time, in different "sub-teams". Currently in the Tour de France there are nine members of any team, although in the past there have been ten or more. In smaller races there are sometimes less than nine on a team. In teams with smaller budgets than a Pro Tour team (the very best), there might be only 15 or less under contract.