In Spain 86% of phone buyers buy from the top 5 brands. Pixel is not among those. Only 1.7% buy Pixel phones. Police say that they have observed that among criminals the percent with Pixels is much higher.
Suppose police have a dead store clerk and only 3 people who could have possibly done it, and those people are 1 Pixel owner, 1 Samsung Galaxy owner, and 1 Apple iPhone owner. Given that criminals are buying Pixels at a rate higher than the general population does, and assuming they are not buying Galaxies and iPhones at a higher rate, can the police use that in statistically valid way to help their investigation?
The answer is yes.
Let (c) = the probability that a random phone owner in Spain is a criminal.
Let (p) = the probability that a random phone owner owns a pixel, which is 0.017 in Spain.
Let (p|c) = the probability that someone owns a Pixel given that they are a phone owning criminal. Police say that this is higher than 0.017, but they do not give a number. I'd expect they wouldn't really notice if it was only a little higher. I'd guess it would need to be at least 0.05 for them to notice, so let's go with that. If someone finds a better number it is easy to adjust in the following calculations.
Let (c|p) = the probability that someone is a criminal given they have a Pixel.
Bayes' Theorem tells us that (p|c)(c) = (c|p)(p).
Rearrange that to get (c|p) = (p|c) (c) / (p). Plugging in 0.05 for (p|c) and 0.017 for (p) gives:
(c|p) = 2.9 (c)
In our case with 3 people to investigate, one with a Pixel and two without, if we are sure that one of them must be the criminal the probability that it will be the Pixel owner is 59.2%. It is 20.4% for the Galaxy owner and 20.4% for the iPhone owner [1]. If the police don't have the resources to investigate all 3 in parallel they should check out the Pixel owner first.
[1] Actually, I don't think that is quite right. I think that because I added the condition that we are sure it must be one of them the distribution will change slightly. It still should be close though.