unlikelihood

[uhn-lahyk-lee-hood]
noun
the state of being unlikely; improbability.

Origin:
1475–85; unlikely + -hood

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Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
unlikely (ʌnˈlaɪklɪ)
 
adj
not likely; improbable
 
un'likeliness
 
n
 
un'likelihood
 
n

Collins English Dictionary - Complete & Unabridged 10th Edition
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Example sentences
Nothing proves the unlikelihood of reforming the faculty unions more than their
  refusal to address the contingent faculty crisis.
Even a cursory glance at the available evidence points to the unlikelihood of
  such a scene.
But the film never gets past the unlikelihood that its characters have much
  chance of living happily ever after.
Many employees never challenge decisions made at the facility level because
  they are discouraged by the unlikelihood of success.
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