How long after dropping did you go into labor?

So I had a feeling that I had dropped last week (my breathing was generally easier and my heartburn had virtually gone away). My midwives have been telling me to not expect labor until AT LEAST week 40 since I'm a first time mom& they looked a bit skeptical when I had mentioned sparadic contractions and that he had felt a lot lower - that is until they measured my uterus. Since the last week it had dropped by almost 3 centimeters. (Went from 36 to just over 33)