Well, in my opinion it depends upon your first assumption regarding the water. If for example the water is rain water on a regular street with no obvious source of najasah, then your fist assumption is that the water is not-najis and you act upon it unless you discover otherwise.
It is not enough to have a suspicion of some rare event (e.g. urination) to have occurred to consider that the water is najis. You need to witness it or have two trustworthy persons inform you.
Off-course if the najis-causing event is frequent in that place, then you would assume the water to be najis.
Also, if the rain-water is plentiful, then I would consider it to be not-najis even in events where a small amount of najasah be present. For example, if one sees another urinate in an otherwise not-najis plentiful stream of water, then the water is considered not-najis. (i.e. urination in a river does not cause the river to become najis)
This is my personal understanding from the shia sect.