The most common and most likely answer to this crossword clue is the 3 plus 6 letter word NOT LIKELY
I've seen this crossword clue in The Times
N
O
T
L
I
K
E
L
Y
Buddy explains!
The straight part
We know that "Improbable/I completely refuse" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case improbable/i completely refuse = not likely.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.