Riot uses multiple methods of detecting the various forms of cheating/botting present in League of Legends. To protect the "trade secret" (i.e. not allow their detection techniques to fall into malicious hands), they do not release information about how it was detected that your account was using prohibited programs/macros/etc.
Some common problems are if you ever installed them, even to try on a different account/in custom games, if you have any sort of macro programs in use that may be accidentally active during a League game, if you ever logged in on a computer other than yours that may have had prohibited programs installed, etc.
The bottom line is you're responsible for all activity on your account, and Riot has a strict zero tolerance policy for any program which macros or interferes with critical game files/operation from the time the client is opened to the time the client is closed. If you have ever violated that policy, even months ago, the ban won't be removed.