Suspiciousness is a quality of distrust or disbelief. Your suspiciousness about your upstair's neighbor's claim that he doesn't have a dog is completely justified if you wake every morning to the sound of barking overhead.
If you're feeling doubtful about whether someone's telling you the truth, or have a hunch that they're up to no good, you're experiencing suspiciousness. Sometimes this quality of being suspicious makes sense (like your suspiciousness when your new classmate claims to be British royalty). Other times, it's okay to question your suspiciousness — that charismatic political candidate's promises may actually be sincere!