Regular "не" always works as "minus with minus makes plus".
For example: "Не задавай ненужных вопросов" - "Do not ask unrelated questions" means "Ask related questions" after all.
But pay attention to "ни-words" (they are used in almost all phrases with negation) - they works as I described above - always are paired with negatives to form negatives.
Because "nobody" - "никто" is "ни-word" we need to rephrase to make positive meaning with two real "не": "не было тех, кто не разговаривал" (there weren't (people) who didn't talk)