Also, the probability of being elected president is definitely not evenly distributed across the U.S. population:
1. If you have no prior political experience (e.g., you've never been a governor, U.S. senator, mayor of a major city, etc.), you probably won't get elected unless you're wealthy enough to be able to spend $100 million of your own money on your campaign.
2. If you're less than 35 years old, or were not born a U.S. citizen, you have a zero probability of being elected president since you don't meet the constitutional requirements to hold the office.
3. If you come from certain ethnic or religious groups, your probability of being elected are greatly diminished. The U.S. has only had one Catholic president (JFK), and no Jewish or Muslim or atheist presidents.
4. If you're not good at public speaking and TV appearances, you'll never be elected president.
I expect that my own probability of being the next president is zero, but my probability of winning a lottery (if I ever buy a ticket) is some very small positive number.