Absinthe saved Xiaolan because she was grateful for being saved, and saved Conan because she admired Conan’s mind and also liked to play detective games with Conan.
Absinthe refers to Belmode, a character in the Japanese comic "Detective Conan" and its derivative works.
Related information:
"Detective Conan" is a long mystery comic created by Gosho Aoyama. It was serialized in "Weekly Shōnen Sunday" in 1994. The single volume is published by Shogakukan in Japan, Changchun Publishing House in mainland China, and Qingwen Publishing House in Taiwan. The simplified Chinese electronic version is published by Tencent Animation, Bodong Planet, and Bilibili Comics. The work tells the story of Kudo Shinichi, a genius high school student who was forced to drink a mysterious poison and turned into an elementary school student Edogawa Conan. While searching for the antidote, he solved the murder of Zong Zong.