definitely vs by all odds

definitely and by all odds both are adverbs.

Word	Noun	Adjective	Verb	Adverb
definitely	No	No	No	Yes
by all odds	No	No	No	Yes

As adverbs, definitely and by all odds are synonyms defined as:

Other synonyms of definitely include decidedly, emphatically, in spades, unquestionably.

definitely (adverb)	by all odds (adverb)
without question and beyond doubt	without question and beyond doubt