There is no Smoke without Fire
We may sometimes find some things extremely difficult to believe. But when it is supported by evidence, we have to believe it. When the impact is seen we are able to infer the cause. There may be no impact without a cause. Fire is the only cause of the smoke. Therefore when we see smoke but no fire, we can safely conclude that there is a fire causing it. This proverb is based on this fact. It generally refers to rumors. The rumours cannot be completely false, there must be some truth in it, however little.