It depends on what priors you put on things like planetary size and orbital periods. If your prior is uniform, then it is just as likely for this configuration to exist as any other and because the probability mass is uniformly distributed (e.g. every outcome is equally likely) then there's probably only one of it.
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.
