It can and does happen, although I'm not sure anyone can give you a percentage. I'm not sure anyone has ever kept track of the numbers.
You may want to make sure that your cholesterol levels are kept well within the recommended limits which can sometimes help in diminishing post-surgical stone/sludge formation. Another factor is suggested to be the use of hormones.
At 26, with no personal or family history of gallstones, I developed a rather painful case of gallbladder disease. At the time I was active and otherwise healthy, and followed a primarily vegan diet. The only recent change to my body was that a year prior I began taking the oral contraceptive Yasmin. I stopped taking the hormones immediately after my first attack. I had several more attacks within the 3 month period before my surgery, each time having acute hepatitis and pancreatitis. About 15 months after my gallbladder was removed my primary care physician and I decided to try oral contraceptives again. Bad idea. Within 6 weeks I had another attack and found myself back in the hospital because of elevated liver counts and pancreatitis. Needless to say, I'm done playing "guinea pig" with my body. I will not be adding hormones to my body ever again, if I can help it.