A quick question about needing a c section and dilation?

I know no one can say for sure because emergency's happen but just wanted some opinions. I am due July 3rd my pregnancy has been 100% healthy and normal. Absolutism no problems. My baby is dropped and head down as well. I am 37 weeks right now. Since all this is good I was just wondering what my chances of c section are? I am getting an epidural and am aware this may cause a c section but since me and baby are healthy I wasn't sure. I want a vaginal birth. I'm not against c sections and will do it if I need to but it is not how I want my baby to be born. Also at 37 weeks is it normal to be completely closed and not dilated? I have no signs of labor or anything but my baby dropped at 33 weeks and went head down at 35 weeks. Does this mean I will most likely go to my due date or over? Thanks for any help or advice. I am a first time mom so I am curious about everything.