Interestingly, it is sometimes humanity's worst people who seek salvation most earnestly. If they have committed grievous deeds and have a conscience, they know they are utterly lost and can do nothing to atone for their actions, so they seek salvation from an external source.
For the rest of us respectable people, we greet such searching with admiration. We hear about someone who was down and out who found religion and we think, "Good for them." We're glad they're doing what they're doing. But what they're doing is "for them." Meaning "not for us." We don't think of salvation from an external source as being as necessary for us, because we're not like "them," because we're doing alright for ourselves.
Even we Christians, who profess to sin and hell and salvation, don't often feel as lost as we really are. And you wonder why non-Christians are annoyed at our proselytizing. Telling others about the way to salvation when we ourselves don't believe deep down that we needed much help to be saved just comes across as haughty and narrow-minded and insensitive.
If you know your Bible, think instead of Isaiah having his encounter with God in Isaiah 6 or Peter having his encounter with Jesus in Luke 5. These two men were face to face with holiness personified and became utterly unglued in its presence: