Becaue the -ㄹ conjugation of a verb represents possibilities and potential (something to come), -ㄹ 것이다 implies some uncertianty. But this uncertainty can vary greatly from quite a lot to near zero in some cases depending on the meaning of the sentence and extra things like adverbs. The important point is, though, that there is no future tense form that is more definite than -ㄹ 것이다. -겠다 is more about a person's intention (가겠다고 한다) or a spontaneously and subjectively observed possibility (이러다가 시험에 떨어지겠다). I don't think it can be classified as a pure future tense like -ㄹ 것이다. We also use the present tense for things that are certain to happen or what we very firmly intend to do in the future (more than in English, I think). For example, we say 나(는) 내년이면 서른이야 (I'm thirty next year) instead of 서른일 거야 because the phrase involves no uncertainty. Compare these as another example: - 나는 내년에 유학 갈 것 같아. uncertain future. - 나는 내년에 유학 갈 거야. (fairly definite) future (with an inkling of intention). - 나는 내년에 유학 가. quite certain future - arrangements have already been made. And saying things in the future tense with less certainty can often increase politeness. But -겠 is more often used for this purpose because one of its major uses is to reduce the directness of meaning. An example in formal setting (in an informal setting, we're likely to use 갈게(요) rather than 가겠어(요)). - 저 갑니다 = I am leaving (now). Curt and business-like. - 저 갈 겁니다 = I will be leaving (slightly unnatural becuase it has too much future sense). - 저 가겠습니다 = I am going to get going. (polite and formal, but somewhat direct in expressing one's intention). - 저 가 보겠습니다 = (slightly more polite - 보다(do something tentatively) here makes for indirect and polite speech).

probable future tense doesn't give a sense of being more polite. The politeness is shown by the ending suffix. e.g. 겠어,겠다,겠어요,겠습니다. ㄹ거야, ㄹ거다,ㄹ거예요, ㄹ겁니다. We can show definiteness by adding some adverbs like 반드시, 틀림없이, 꼭, 기어이, 기필코, 결단코, 맹세코, 확실히, 분명히. e.g. 이번엔 꼭 이기고야 말겠다 This time I'll win at any cost. 반드시 참석하겠습니다 I will be present without fail. 나는 기필코 그것을 해낼 것이다 I will carry it out at any cost 그녀가 들으면 틀림없이 기뻐할 것이다 She'll certainly be happy to hear that. We can show uncertainty by adding some adverbs like 아마(도), 어쩌면 e.g. 그는 아마 못 올 것이다 He probably won't be able to come. 우리는 아마도 이틀정도 일찍 떠나야만 할 거에요. We should probably leave a couple of days early.