The fact that I received a letter conditions the probability distribution of the number of letters sent, raising the expected value.
   
Groucho Marx famously said that he would never join a club that would have him as a member.  There is a similar result in probability:  if I choose a random subset of the population with a random size, and you discover you are in the set, then that information raises the odds of a large set and lowers the odds of a small set.
 
For example, if I pick a random number equiprobably from 1 to 100 and mail that many letters out, the expected number of letters is 50.5.  But if you find out that you've received one, the expected number of letters jumps to about 66.