The new series starts on Tuesday 29 October at 8pm so is a 100% clash with Bake Off. I think that's what happened last year. Marcus Wareing and Monica Galetti back as is Gregg Wallace though he tends not to be in every episode.
Episodes also on Thursday and Friday at 8pm,
Series lasts for 7 weeks as normal.
Bake Off's final episode is on 26 November. So if Professionals gets shown each Tuesday there's a clash for the first 5 weeks,
Regarding Big Brother, the rumour is that it lasts for 6 weeks which would mean that the final is on Friday 15th of November, so a partial clash with Bake Off for another 4 Tuesdays