NNT is calculated assuming that the patient has the condition being treated. NNT* is calculated when there is uncertainty about whether the patient has the condition. You can interpret NNT* as the number of patients *just like this one* who I have to treat to prevent one bad outcome. The flu prevention in household contacts is a little more complicated. The NNT* there refers to how many *household contacts* you need to treat to prevent one case of the flu.
Remember that NNT is just 1/ARR. You might find it easier to think in terms of ARR. If the ARR of treating is when I'm sure the patient has the disease, then if the patient has probability P of having the disease, ARR* = PxARR and NNT* = 1/ARR*.