Doubt in Assumption 1 of random sample

In this 1st assumption, the independence must be pairwise or overall?. Coz in the example of cards. The population consists of `52 C 13` elements. out of which ¼ th elements have king of diamonds(True) and rest of them are (False). So suppose I am creating the elements of this population one by one till the population size becomes `52 C 13`. and suppose there comes a point where I have created all these ¼th elements which contains king of diamonds. So now I am 100% sure that all the elements created after this will not have king of Diamonds. Then how are these elements Independent?