Finely tied, no doubt (10)

I believe the answer is:

definitely

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'no doubt' is the definition.
Both the definition and answer are adverbs. Perhaps they are linked in a way I don't understand?

'finely tied' is the wordplay.
'finely tied' can be anagrammed to 'DEFINITELY'.
However, I am unsure how the anagram is indicated.

Can you help me to learn more?

(Another definition for definitely that I've seen is " without question".)

I've seen this clue in The Irish News.

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