The killer is
Keizo Masuo. Knowing his wife's daily routine, he set a knife hidden on the top of the bookshelf and tied it to his wife's exercise bike with a thin rope. The string was wound around the pedal and would eventually pull the knife from the shelf, stabbing Kayo in the process. To establish an alibi, Keizo called his wife from the police station and had her talk to Takagi shortly before she "was attacked". Once the police arrived at the scene of the crime, Keizo instructed Takagi and Sato to check upstairs while he went to the living room where Kayo's body is to eliminate the evidences. Unfortunately for Keizo, he accidently pricked his finger while removing the pin used in the crime in order to hide the string inside the bike. If the blood on his finger and the bloodstain on the shelf match, then it will be proved that he is the one who set up the trick to murder his wife.
Cornered, Keizo admits his crime, claiming that he and Kayo had fallen out recently thus he decided to kill her. However, Sato correctly deduces that Keizo's true motive is actually to cover his role as the mastermind behind the robbery crime at the branch under his management.
Motive
The robbery was actually set up by Keizo as he was under financial trouble due to his wife's lavish lifestyle. The plan would have gone smoothly had it not for Kayo happening to visit the bank on that day. While being taken hostage, Kayo recognized the robbers as her husband's friends and not knowing that he was infact the inside man, which was the reason why the robbers switched hostage.
Afterwards
Afterwards as Shiratori is being praised by Chief Matsumoto, Sato says that "such matters" were solved by Conan. Shiratori concedes that children notice things they do not. Later Shiratori ask Sato lunch as an expensive restaurant but is denied. Once Shiratori leaves Sato invited Takagi to a ramen restaurant, but Takagi is left behind after Maguire inites her to join for a drink. Takagi is moping as the Detective Boys ask about when he's going to take their testimony.
Hostage situation (past)
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Location:
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Tohto Bank, Haido Branch
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Victims:
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Kayo Masuo and Midori Megure
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Age:
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42 years old (Kayo)
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Time:
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3 days ago
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Culprits:
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Unnamed two robbers
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After being taken hostage, Kayo recognized the robbers' identities. She then tried to free herself, prompting Inspector Megure's wife, Midori to offer herself as a hostage since she was at the bank at the time.
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When Kayo planned to bring an album containing photos of Keizo's friends to the police, Keizo killed her out of fear as if his friends were to be arrested they would reveal Keizo the mastermind behind the crime. Two hours later, the two accomplices, who are quietly counting their money, are arrested and both cases are solved at once. Conan comments that in a strange twist of fate, Kaizo had to kill his wife because of the robbery, since it was due to her that he had set the robbery in the first place.