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Shinichi/Conan and Azusa are kidnapped. While Shinichi/Conan is unconscious, Azusa finds a severed head in a jar.

Shinichi/Conan was faking being unconscious, waiting for a chance to turn the tables.

The "head in the jar" is an elaborately-arranged laminiated photo, and the severed finger is just an elaborately-cut sausage.
The kidnappers are editors of a game magazine who kidnapped Azusa because they thought she would leak info about a game that hadn't released yet and get them in trouble with the game company.