Conan wrapped his arms around his mother's leg for good measure -- he hated having to act like such a kid in front of people he knew and people he didn't know, but it did well to help keep his cover up. Not like any Black Org agents would be hiding here, of all places, he thought blandly, his eyes scanning the area suspiciously.
"O-oh," Oshiro immediately backed down, hiding her purse behind her back. "I... I didn't mean it, really," she laughed nervously. "It was just a joke! Right, little boy?"
Conan sniffed, still hiding behind his mother. Right. Not asking that woman any more personal questions. Hattori or his mother could deal with her if needed.
"Hey, boy, if it's important, I'll answer it without a fuss," Tachibana laughed. She sounds like a witch, Conan thought to himself. Of course, he would never say something like that out loud -- even he knew better. "If you're curious, Yamauchi and I aren't together anymore simply because I broke it off. I thought that maybe we were getting a little too dependent on each other, so I figured that we could use a little break. But then of course when I was about to propose getting back together, he started going out with some other sleazy chick," she scoffed. "So forget that."
"Thank you, Onee-san..."
So all three had possible motives: Oshiro could have been so angry over his comments about her physical appearance that it would drive her to murder (a very stupid reason even as stupid motives went, but it couldn't be disregarded -- he'd heard crazier ones), Izumi was upset over the cheating, and Tachibana had similar reason.
Conan ran the possibilities through his mind. Oshiro's alibi was not able to be proven. Izumi had a more firm one, but with the lack of a solid time, it was still shaky. And Tachibana's was still under future judgement.
"We're here!" Tachibana said suddenly, and Conan stopped to see what kind of game stall they were at. It was one of those tossing games, where the player would be given up to three rings and thus had three chances to get it around a glass bottle. "I was playing here when my boyfriend's stomach started to hurt."
"Excuse me, Oji-san!" Conan maneuvered around his mother's body to tap on the stand. "Do you recognize this woman?"
"Hm? Yes, I do! Why do you ask?" The man smiled down at him.
"Do you know what time it was, and was she with a man she seemed really familiar with?" He had to prove the boyfriend even existed, after all.
The man pondered for a moment before nodded. "It was around an hour and a half ago, and she was holding hands and laughing with a young fellow. Poor man, though -- he suddenly started to look very sick and quickly excused himself to run off somewhere."
"That was around when his stomach started to hurt," Tachibana confirmed.
Conan nodded, beaming up at the man. "Thank you, Oji-san!" He turned away and put his chin in his hand. So she was here around the time of the murder, the man remembered her boyfriend and even mentioned what happened to him without prompt... Tachibana's alibi checks out.