Which episode of Conan draws lots?

Signing a contract means that Conan's identity will be discovered by Xiaolan. Conan also thought of this at that time, but felt that there was no reason to be discovered by Xiaolan, so it was impossible. Hattori was just joking with Conan. The signs there should be very accurate, but Hattori should have said so on purpose because he was aware of Conan's thoughts.

Later, on the boat, Conan thought that the sign said that Bai Niao (Kidd) would find him a freshman. But actually it was discovered by Xiaolan, and later, thanks to Kidd, she was able to escape.