P(you heard about someone noticing|it’s true) = P(you would have heard someone noticed|someone noticed) * P(someone noticed|it’s true)
The problem with the way a lot of people use that is that they compute P(someone noticed|it’s true) using someone=”anybody on earth”, and P(you would have heard someone noticed|someone noticed) using someone=”anyone among people they know well enough to talk about that”.
The problem with the way a lot of people use that is that they compute P(someone noticed|it’s true) using someone=”anybody on earth”, and P(you would have heard someone noticed|someone noticed) using someone=”anyone among people they know well enough to talk about that”.
Also “someone would have noticed” isn’t the same thing as “someone would have noticed and talked about”.