The approach is formally correct. You always have to make sure these values actually exist, but otherwise it goes through.
The example is probably not the very best, but P(D) may make more sense if you think of the following:
If D equals the amount of coffee I put in the grinder, then D has a certain random component. Sometimes I put in more, sometimes less - even though I aim at a specific level. This is why it is important to have a concept of P(D) in Bayes' equation.
The one case where I inadvertently put in a lot of coffee should not be used for "strong evidence" - is the idea here.
The example is probably not the very best, but P(D) may make more sense if you think of the following:
If D equals the amount of coffee I put in the grinder, then D has a certain random component. Sometimes I put in more, sometimes less - even though I aim at a specific level. This is why it is important to have a concept of P(D) in Bayes' equation. The one case where I inadvertently put in a lot of coffee should not be used for "strong evidence" - is the idea here.