Question: What is a single word to convey the sense of "inaccurate suspicion," but that tends to infer a bit of unfairness, such as 

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> It is immoral to use brutal force in response to [inaccurate suspicion].
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Answer: 
Inaccurate suspicion is supposition, but, as commented below, I think **misconception** is closer in meaning to the above question which is dealing not with a prior, unvoiced, suspicion but is about a suspicion that becomes active - so misconception would then be more appropriate, I feel.

***Misconception***

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> A view or opinion that is incorrect because based on faulty thinking or understanding.‘public misconceptions about antibiotic use’
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[Oxford Dictionary](https://en.oxforddictionaries.com/definition/misconception)

> 
> supposition
>  ˌsʌpəˈzɪʃ(ə)n/Submit
>  noun
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> a belief held without proof or certain knowledge; an assumption or hypothesis.
>  "they were working on the supposition that his death was murder"
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[Google Dictionary](https://www.google.co.uk/search?q=supposition&oq=supposition&aqs=chrome..69i57j0l5.3036j0j8&sourceid=chrome&ie=UTF-8)
The precisest word in English to this concept is "surmise".

* The OED defines: "To form a notion that the thing in question may be so, on slight grounds or without proof; to infer conjecturally."
* A surmise is (obsoletely) "An allegation, charge, imputation; esp. a false, unfounded, or unproved charge or allegation."
* A surmiser is "One who makes a surmise or conjecture (esp. ill-founded); [...] one who suspects evil of another."