ecbphotos/iStock/Getty Images PlusFollow ZDNET: Add us as a preferred source on Google.Just how private are the conversations you have with your favorite AI?Last week, news broke that conversations from Anthropic's Claude AI could be accessed through a Google dork (translation: advanced search query). Yes, people had already shared these conversations with others via active links. But I'm sure they never imagined that the topics discussed could be exposed to anyone with some search savvy.Also: 5 reasons you should be more tight-lipped with your chatbot (and how to fix past mistakes)Anthropic quickly fixed the "exploit" to disable this type of indexing. But the question remains: Just how private are your AI conversations? In part, that depends on you. Though the AI companies don't always make it easy, they do offer controls through which you're able to manage your own privacy.Toward that end, let's look at four major AI chatbots and cover steps to tighten your privacy as much as possible.ChatGPT Don't want your conversations in ChatGPT tracked or saved? You can chat with the AI without an account. Even if you have one, just log out before you submit your query. Certain advanced features won't be available, and you'll hit lower thresholds. But if you don't want to expose specific conversations, this is certainly an option.