Due date tomorrow with posterior cervix :(

I got checked today at 39+6 weeks and my OB said that my baby's head is really low, my cervix is soft but it's posterior and closed. I was supposed to do a sweep but she couldn't do it. She scheduled me for an induction next week. What are the chances that I'll be able to go into labour before then? Anyone experience this before? It was kind of disheartening because I could tell that my baby has dropped and was hoping I would atleast be a cm dilated.