If you don't like the phrase "uncertainty about the probability", think of it as a probability that is made up of particular kinds of multiple components.

The second sweepstakes example has two components, uncertainty about which entry will be picked and uncertainty about whether the manager is honest. The first one only has uncertainty about which entry will be picked. You could split up the first example mathematically (uncertainty about whether your ticket falls in the last two entries and uncertainty about which of the last two entries your ticket is) but the two parts you get are conceptually much closer than in the second example.

. In this case, the probabilities are bounded below by a not-ridiculously-small number, that (Robby claims) is high enough that we should not eat meat.

Like the possibility that the sweepstakes manager is dishonest, "we don't know enough about how cattle cognize" is all or nothing; if you do mulitple trials, the distribution is a lot more lumpy. If all cows had exactly 20% of the capacity of humans, then five cows would have 100% in total. If there's a 20% chance that cows have as much as humans and an 80% chance that they have nothing at all, that's still a 20% chance, but five cows would have a lumpy distribution--instead of five cows having a guaranteed 100%, there would be a 20% chance of having 500% and an 80% chance of nothing.

In some sense, each case has a probability bounded by 20% for a single cow. But in the first case, there's no chance of 0%, and in the second case, not only is there a chance of 0%, but the chance of 0% doesn't decrease as you add more cows. The implications of "the probability is bounded by 20%" that you probably want to draw do not follow in the latter case.