They might think that or they might simply hope that it is true. It isn't on the level of thinking for most, it is faith which requires no proof whatsoever. Coincidence isn't taken into account when someone searches for ways to justify their faith in prayer for example. The problem is that faith shouldn't be justified, it is a way of being insane or delusional to some people.
Either way it never hurts to pray for someone and it is a genuine way to feel compassion for someone when it is difficult to do so normally. Prayer is basically meditation anyways attached to a conversation with something specific like a god. When some people pray it can put them in an almost asleep dreamlike state where they are really relaxed.
Nothing cares about what underwear you have on, it is nonsensical. Football teams praying for victory is stupid as fuck. IMO praying for stuff that is meaningless in the grand scheme of things is a waste. When someone prays for something stupid and meaningless, God probably listens then laughs. Whether God does anything about it is another matter entirely.
The whole shape the world around me through the power of my will thing is fun to think about. I have yet to see someone myself really achieve anything close to using their willpower to do the scientifically impossible. I have seen prayers answered that were against huge odds, but you can chalk that up to coincidence somewhat.
phobia.