Probability of Flush Given 3 clubs on flop

[Todd Terry]

This was inspired by a post in HSMTT. The problem I'm posting here is slightly different. Seven handed game, all see the flop, assume random distribution of cards for all seven (that is, don't use conditional probabilities based on the fact that they chose to stay in to see the flop). Flop comes out 3 clubs. What is the probability that one or more players has a flush?

I came up with 24.75652%. It took fairly serious number crunching to get it. I want to see if I got it right, and see if anyone comes up with a solution that arrives at an answer more efficiently than mine did.