The most common and most likely answer to this crossword clue is the 9 letter word OBVIOUSLY
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More clues leading to the result OBVIOUSLY
Buddy explains!

The straight part
We know that "Without a doubt" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case without a doubt = obviously.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does OBVIOUSLY mean?
OBVIOUSLY adverb- In an obvious or clearly apparent manner.
- Used as a filler word, or to introduce information even when not obvious.