Explanation:

- "There is no smoke without fire" is a common idiom. It means if there is an indication of a problem, the problem likely exists.

- Option 1: "with" doesn't fit the idiom. "No smoke with fire" isn't a recognized phrase.

- Option 2: "within" would suggest smoke inside fire, which isn't the intended meaning here.

- Option 3: "where" would indicate a location, not fitting the idiomatic expression.

- Option 4: "without" correctly completes the saying, "There is no smoke without fire."