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Throughout the last Sherlock episode of the 4th season, The Final Problem, characters are motivated to help a little girl on a plane who is apparently the only awake passenger. The pilots and all other passengers onboard are asleep.

However, no one seems to ever question whether this is even plausible. Given they are spending most of the episode in Eurus's mind game, it seems strange they never once question whether this is actually happening in reality.

The circumstances of the plane/girl seem absurdly unlikely yet Sherlock visibly and emotionally is worried about her in many of his interactions with her.

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There's probable a combination of reasons based on the situation:

  • It seems like something Eurus would do

When Sherlock first confronts Mycroft in his house about his sister, John tells him that he was shot with a tranquilizer and Mycroft doesn't seem surprised. It's possible that she had an affinity with either narcotics (like Sherlock does) or putting people to sleep, as she does to John and then to all three of them later on.

This means that her putting an entire plane of people to sleep (except for the girl) is plausible based on her character.

  • They had no reason not to believe her

Eurus caused the governor to commit suicide right in front of them, and then they witnessed Eurus killing his wife immediately afterwards. They then saw an additional three people die through the window, and she didn't even blink. Killing a plane full of people would have meant nothing to her.

She also managed to take over the prison, and then fly a drone with a highly advanced weapon attached to it, so clearly she had the means to set up something so complex.

She needed something to motivate them to continue with the game, and they believed that she was capable of setting up the plane situation without concern for the passengers, so they had no reason to suspect she wouldn't do it. It would have been as straightforward for her as setting up any of the situations that they were put in.

  • They're in a high stress situation

With the pressure of the situation on top of them they wouldn't have had time to stop and process what was happening fully. They had a short time limit to complete the tasks and to try to help the girl, so they weren't able to realize that the mind game was, itself, a mind game.

  • To add a tiny bit to your argument It seems like something Eurus would do: It is also very reminiscent of what Moriarty did in The Great Game. – Wrzlprmft Feb 16 '17 at 3:28

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