improbability

1. The quality or condition of being improbable.
2. Something improbable.

Definition: unlikelihood
Antonyms: certainty, probability

n.

    His tale he told with a solemn face
    And a tender, melancholy grace.
        Improbable 'twas, no doubt,
        When you came to think it out,
        But the fascinated crowd
        Their deep surprise avowed
    And all with a single voice averred
    'Twas the most amazing thing they'd heard --
    All save one who spake never a word,
        But sat as mum
        As if deaf and dumb,
    Serene, indifferent and unstirred.
        Then all the others turned to him
        And scrutinized him limb from limb --
        Scanned him alive;
        But he seemed to thrive
        And tranquiler grow each minute,
        As if there were nothing in it.
    "What! what!" cried one, "are you not amazed
    At what our friend has told?"  He raised
    Soberly then his eyes and gazed
        In a natural way
        And proceeded to say,
    As he crossed his feet on the mantel-shelf:
    "O no -- not at all; I'm a liar myself."

The noun has one meaning:

Meaning #1: the quality of being improbable
  Synonym: improbableness
  Antonym: probability (meaning #2)