1. These three words can be commonly used interchangeably. 분명한 증거/ 명확한 증거/ 뚜렷한 증거 2. Especially for 분명하다, 명확하다, I would say these are the exactly same meanings and you don't need to hava any worry about using them interchangeably. However, 분명 can be more casually used in daily conversation. ex) 그가 오고 있는 게 분명해. It's certain that he's coming. 당신의 의견을 명확하게 밝혀 주세요. You should voice out your opinion clearly. 3. There is just one thing to let you know between the two. 분명히 말하는데, 분명하게 말씀드립니다. are more idiomatic expressions. When you want others to listen to you and not forget what you're saying, you can say those as a warning. But, this can be a threat depending on a context. ex)분명히 말씀드리는데, 먹이는 하루 두 번만 주세요. 아니면 죽어요. (I'm warning you. Feed them only two times a day, or they die.) Or if you want others to be aware of the fact that you've already warned them, and the result is not your fault, you could say in a past tense. 분명히 말했다. ex) 스키탈 때, 고글을 착용하라고 분명히 말씀드렸어요. (I've wanred you that you need to wear goggles when skiing.) ---->In this case, 뚜렷 sounds awkward. 명확 can be used but 분명 sounds more natural. 4. we commonly use '뚜렷하다' when describing someone's face. If someone has clear-cut features in his/her face, we would say 이목구비가 뚜렷하다. In this case, you could say 분명, 명확 but I think 뚜렷 would sound more natural. This is a kind of idiomatic phrase. To a simple conclusion, it might be easier to understand like this. 분명 can be used commonly, casually, and can replace 명확, 뚜렷 명확 is a little less casual. 뚜렷 can describe some features or lines.

* 분명하다 = clear or distinct (분=distinct/divisible, 명=clear). Not confusing or in doubt. (분명하다 is used for anything that is clear - I don't think there is any preference for sight-related things) * 명확하다 = clear, definite (명=clear, 확=certain, definite). * 뚜렷하다 = distinctly identifiable. This word has a preference for visual and other sensory perception. 분명하다 and 뚜렷하다 are more common, in both colloquial and formal contexts, while 명확하다 is used a little more formally. 뚜렷하다 is frequently used for direct perception than logical reasoning. Even when referring to memory, it seems to imply that the speaker remembers it like he sees or feels it. * 그 사람의 의도는 분명하다 = His intention is clear (beyond any doubt). * 질문에 분명히 대답해 주세요 = Please give a clear/unequivocal answer to the question. * 명확한 논리의 전개 = Chrystal-clear derivation of logic. * 멀리에 차의 모습이 뚜렷이 보였다 = The figure of a vehicle was clearly visible in the distance. * 지금도 그날을 뚜렷이 기억한다 = I still remember that day clearly (like I see it).