How are clothes and vessels purified from the impurity of dogs, and is impurity transferred merely by touching a dry dog vessel?

A garment or body part must be washed seven times, one of them with earth, if it is touched by a dog's saliva or mucus, or if anything from its moist nose, urine, or excrement gets on it. This is based on the hadith (definition): "If a dog licks a vessel belonging to one of you, he must wash it seven times, the first time with earth." However, if a dog merely sniffs a garment without touching it, or if the dry part of the dog touches the garment or body, then washing is not necessary, because the mere contact of a solid impurity with something pure does not render it impure, unless you are certain of the impurity or strongly suspect it. One must be wary of obsessive thoughts.