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No shadow of a doubt the director of public prosecutions will appreciate this (10)

Ross

I believe the answer is:

conviction

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This could be a double definition.

'no shadow' is the first definition.
The definition and answer can be both related to thinking as well as being singular nouns.
Perhaps they are linked in a way I don't understand?

'a doubt the director of public prosecutions will appreciate this' is the second definition.
The definition suggests a singular noun which matches the answer.

'of' is the link.

Can you help me to learn more?

(Other definitions for conviction that I've seen before include "No doubt" , "Strong belief" , "Certainty" , "it follows proof of guilt" , "Firm belief" .)

I've seen this clue in the Irish Times and the Irish Times (Crosaire).
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