1) Implausibility 2) Implausibleness 3) Improbability 4) Incredibleness 1) Incredibleness 2) Quality 
• (n.) The quality or state of being incredible; incredibleness. • (n.) That which is incredible.
In·cred`i·bil'i·ty noun [ Latin incredibilitas : confer French incrédibilité .] 1. The quality or state of being incredible; incredibleness. Dryden. 2. That which is incredible. Johnson. 
[n] - the quality of being incredible
incredibility The quality or fact of being incredibile; a thing that cannot be believed; an incredible notion or circumstance.
incredibleness noun the quality of being incredible