Do clothes that have been touched by water used to wash an impure shoe become pure?

If water, having come into contact with impurity, splashes onto your clothes, and it has not changed due to the impurity, then it is pure and does not render what it touches impure. However, if it has changed due to the impurity, then it is impure and renders impure whatever it touches of clothes or body, except if it is a small splash, which is pardoned due to its small quantity. As for impurity that affects the bottom of a sandal, it is purified by rubbing it on the ground.