IOW, about the same odds of everyone on the planet Earth winning the lotto simultaneously.
Not at all. The odds against six billion people (choosing independently and randomly) picking the same, say six out of 80 numbers, and then having those numbers selected in a random drawing is less than one with fifty-million zeros after it, effectively impossible. (Assuming you grant everyone one entry.) One hundred to one against events occur every day. Would you get on an airplane that had a one in a hundred chance of crashing?
If it does occur, it will be millions of years in the future. The process would be slow, but inexoriable. Each Mercurial year, Mercury's orbit would become a little more enlongated. Assuming Earth is inhabited by a technologically advanced civilization at that time, they would see it coming millions of years in advance.