no antibiotic is going to wear off in 12 hours to give a probiotic a chance to work overnight. The antibiotics can either kill any culture the probiosis can produce, which makes the probiosis pointless, or the probiosis can evade the antibiotics ( bloody unlikely) and it wouldn't really matter when you took them.
This is why antibiotics are given in courses. 4 days is because you need one or two days of them working, nine days course for a weeks effect, and so on.