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• n  the improbability of a specified outcome

• The better I got to know the Obamas, the more astonished I became at the unlikeliness of Barack's ascension.
• Every year on May 5, paraders in various cities dress up in elegant French uniforms and scrappy Mexico outfits that signify the unlikeliness of the Mexican victory over France.
• They may love her or fear for her, but mostly they simply marvel at her existence, at the delicious unlikeliness of such platinum innocence.

• unlikelihood

• likelihood
• likeliness