As a noun: the act or an instance of suspecting something wrong without proof or on slight evidence.
When suspicion is left unchecked, it fast morphs into distrust. These are not the same thing.
As a verb: to have no trust or confidence in… Unchecked distrust breeds distance. Creating physical or mental distance is a natural, inbuilt, response to a threat – perceived or otherwise.
Investigate suspicions vigorously and without apology, because the alternative may be even more difficult to live with.
Finding the proof, or lack thereof, quickly, is better than stewing in suspicion.