[thaumaturgy]

No, likelihood ("probabilistic thinking") is very relevant, and is a crucial element of effective search management.

No search operation has unlimited resources. If you had unlimited resources available, then sure, you can run down every imaginable possibility. But, real-world, it's not like that: you've got a few groups of people, maybe, who can devote some time to one case, and then they've gotta move on to the next one.

Your scenario is also essentially impossible to disprove. A detective might examine a home computer and find no evidence, but what if he used his phone? What if he used some other workstation? What if he knew someone? There are an infinite number of what-ifs, and striking each one off the list -- which is time-consuming and expensive -- only leads to another one.

There are few certainties in cases like this. All you get is the evidence and your ability to put the pieces together. After that, it's all probabilities.