Run out

Now, I know two wickets can be taken off one ball when the batsman are run out on both the ends. If such a case arises and if the to wickets fall on the last ball of an over, who among the two new incoming batsman will occupy the striker's crease? Can anyone of the incoming batsman occupy the crease or is it dependent on the batting order? These are a few questions that came to my mind when I imagined the above scenario. I tried googling it but didn't find the an answer. If you know the answer, do pen it down in the comments section.