It depends on the type of doctor and lawyer’s service. Some will remain with humans. Some will be a welcome free-up of their time to focus on the more unusual (not solvable by regressing to the mean) cases. There are many doctor’s appointments that boil down to ‘You have the flu. Here’s a beg off note for your shitty boss. Go back to bed.’ And there are many attorneys’ consultations that boil down to ‘I have taken down what you want to say, and now I will translate it into legalese.’

As for the trust, that comes from expectations. You trust a human because human surgeons are the norm. You don’t have buddies who had a robot remove their appendix. If the AI is competent, eventually that would be as normal to a patient as buying something from a vending machine.

However, I suspect surgery in particular is another of those things where it’ll take an absolute mountain of training data and a lot of risk of human health/life to even attempt, so it’s a long way off compared to the simple ‘GP writes a referral’ stuff.