Throw a d6 seven times and the pigeonhole principle requires that a configuration will come up twice. The example is weakening your argument; it's still true that if you throw a d6 five times, you expect a configuration to come up twice.
A better example wouldn't involve a probability that can achieve 1; maybe ask about the probability of rolling a 3, or of rolling another 3 given you've already observed one 3.
None of those will match the comment above; it isn't well posed.
> Throw a d6 seven times and the pigeonhole principle requires that a configuration will come up twice. The example is weakening your argument; it's still true that if you throw a d6 five times, you expect a configuration to come up twice
Even that isn't as strong as you could make it; rolling a die 5 times is basically the birthday paradox but instead of asking 30 people their birthdays to find a duplicate, you're asking 300.
In the case of life supporting planets though, it feels like we're trying to talk about the likelihood of rolling a given value when we haven't even determined whether the die has unique values on each face or not. If you're assuming that only one of the sides has a 3 on it, the interesting part is already over.
Yes, I mentioned that in my comment, unless you believe that after seeing five rolls including a duplicate, adding a sixth might bring the total to six rolls with no duplicates.
Throw a d6 seven times and we expect a configuration to come up twice, even though the distribution is uniform.