Q. Eggs from types of birds such as the eagle would not be kosher, but how can chicken eggs be kosher, since we don’t know the bird is kosher until it has been slaughtered?
In regard to “clean” species, we apply a probability principle. Most birds from such species are kosher; we can use their eggs unless we know the bird has a defect that would make it non-kosher. The same applies to cow’s milk.
Why do we examine the lungs of a slaughtered cow and not rely on the probability principle? Because lungs have a high rate of problems and we want to be sure (Chullin 12a and Rashi).