Just onething from my experience. My bitch Betty is 3 years old and we had exactly the same problem - urine started to drip at the beginning just a bit, then it get worse and worse. Took her to the best vet hospital here - all the tests - nothing. Absolutely clear health list, so - incontinence after spay surgery. Started on hormones and all that - no results at all, it was all going worse.
So my vet suggested just to try out antibiotics - just in case! On the same day the dripping stopped and after she completed the course, it had not had back. No tests were showing any inflamation! 3 or even 4 seems too young for me to get incontinence, so remember my story, just in case if nothing else will be found.