John and Ann run an animal shelter that houses cats and dogs. The ratio of cats to dogs is 5:4. Of the cats, 2/5 are kittens, while 3/7 of the dogs are puppies. The shelter houses a total of 63 animals. A group of 6 animals is chosen at random from the shelter. What is the probability that the group contains at least one kitten? Give your answer to 4 decimal places.