L had a suspicious that you were the second Kira. However; he didn't knew that his subsequent out of elevated curiousity (a one-time thing) would actually prove his accusation with your self-perceived demonstration one day.

Today felt L a bit too eccentric about you – so he decided to follow you. He went all they way (obscured) after you, until you stopped in a secluded area. He waited and waited.. until a look of revelation crossed his face at seeing you ACTUALLY pull out a Death Note.