difference between obviously, definitely, and certainly

obviously - (илэрхий, илэрхийдүү) same meaning in clearly
1 used when giving information that you expect other people to know already or agree with
       ---- Obviously, we don't want to spend too much money.
2 used to say that a particular situation or fact is easy to see or understand
       ---- He was obviously drunk.
definitely - (гарцаагүй, гарцаа байхгүй) "definitely" has an stronger emphasis than certainly
 (informal) a way of emphasizing that something is true and that there is no doubt about it
      ---- I definitely remember sending the letter.
certainly - (эргэлзээгүй) there is no doubt
without doubt      --- Without treatment, she will almost certainly die.

difference between definitely and certainly

• definitely is something definite; beyond any doubts; 100 % likely
  whereas
  certainly is something certain; having no doubts; 99 % likely
  
  He will definitely vote for Y. - No way in hell he'll vote for someone else
  He will certainly vote for Y. - I wouldn't know why he'd vote for someone else

• There is no difference in meaning. Any difference in use is personal or regional preference.

• The words don't seem interchangeable here.
  
  There is a concessive force often in certainly which I don't sense in definitely.
  
  Can I stay up and watch the film on TV, Dad? Certainly you may.
  Can I stay up and watch the film on TV, Dad? Definitely you may.
  
  I put a cross by the second, not because it would be out of the question, but because I think it would be odder than the first from a father in these circumstances. To my ear certainly here suggests more the granting of permission where definitely is a statement of fact.

• There is no difference....Certain and definite are the same...precisely, exactly are two more that have the same meaning.

• Certainly: you're treating with a certitude or an estimated certitude, where you're almost sure it is "that way"
  Definitely: treating with an essential definition, the only way an "object" can be.
  Therefore, definitely has an stronger connotation of "truth". They are almost interchangable but the "definitely" has an stronger emphasis. Take "certainly" as saying something has ALMOST a 100% of probability of being true (still a minimum of being false) while definitely has 100% of being true (it is "true" under all cases)

• certainly is of course and definitely is for sure