How does a fighter know when they are ready to turn pro? Well, I think the answer is a combination of the answers that Judoka and Deadpool have offered. Realistically, it would have to be both of those factors meeting up at the same point.
Firstly, your trainer (especially if they are experienced in handling a professional fighter) should be familiar with the level of skill and performance that is required for a fighter to turn pro. If a trainer knows that their fighter is at an acceptable level of skill, but is not able to perform on a level that is competitive to their prospective opponents they probably won't push to turn them pro. The same goes for the opposite scenario where a fighter can competitively perform well, but their skill level is not up to par with other opponents then they may end up competing but on a low-level only. It's a bit of a balancing act that can't be recognized, neither can it be handled, by the fighter.
The trainer (if they are attentative) is going to be able to objectively and honestly critique and compare their fighter with their competition. It is based off of this that they will be able to know what to concentrate the majority of their training hours to, and develop effective fight plans. In that end, the trainer should be able to make the call as to when a fighter is ready to turn pro.
However, none of this will matter if the fighter themself is confident in their own abilities to fight on a pro level. There are many tough guys in the gym, that never show their abilities outside of the gym. They may not be focused on competing, or they may not want to compete at all. The self-confidence has to be there. You just have to keep in mind that a sense of self-confidence can be real deceiving, thus the reason why a competent trainer needs to be there to keep their fighter's feet planted on the ground.
If all things meet, then you should have a scenario that indicates you are ready to go pro.
It doesn't matter if you agree or disagree
... As long as I don't bore you and I spark a moment of thought, my goal is achieved
Queng leon queng tigre ecu tacacut, queca pa? - Pampangan Mandarigma Motto