Heres a rundown based on what we see so far. In the past Baku played a game (unknown if it was like yukii's labyrinth game) and lost, meaning he lost his alibi for a day, got convicted of something he didnt do and served hard labor for a period of time. The murderer of said case was karusuyama. Now cut to present. Karusuyama is about to be revealed as the real murderer. This will create a paradox, as kakerou had taken the day from baku. If Baku reveals the murderer, it will be as if he is stealing back his "day" from kakerou, something they cannot allow.