pi is a single fixed number, so it doesn't help to talk about probabilities. Either every finite length sequence appears in pi, or at least one doesn't.
The technical term "almost surely" applies to all p=1 probabilities, even those where it's really certain that the event happens. This does not match with common understanding of "almost surely" because we'd not usually make a statement like "the decimal expansion of pi almost surely contains the number 4", but mathematically it's a correct statement.
It's important to keep in mind that this is technical terminology, so intuition does not always apply. It also means that it does not make sense to talk about women being almost surely pregnant without first defining a probability distribution. If we define each woman to be pregnant with a probability of 1%, independent of the pregnancy status of other women, and we have an infinite number of women, then almost surely at least one of them is pregnant. That is, the probability that at least one of them is pregnant is 1. But it's not certain that at least one of them is pregnant, it could be that all of them are not pregnant. Similarly, if we choose a number uniformly in the interval [0,1], then the probability of choosing 1/3 is 0, but it's possible that we chose 1/3. We cannot ignore that as an impossibility either, otherwise when we chose a number x, we could always claim "it's impossible that we chose exactly x!".
pi is a single fixed number, so it doesn't help to talk about probabilities. Either every finite length sequence appears in pi, or at least one doesn't.
The technical term "almost surely" applies to all p=1 probabilities, even those where it's really certain that the event happens. This does not match with common understanding of "almost surely" because we'd not usually make a statement like "the decimal expansion of pi almost surely contains the number 4", but mathematically it's a correct statement.
It's important to keep in mind that this is technical terminology, so intuition does not always apply. It also means that it does not make sense to talk about women being almost surely pregnant without first defining a probability distribution. If we define each woman to be pregnant with a probability of 1%, independent of the pregnancy status of other women, and we have an infinite number of women, then almost surely at least one of them is pregnant. That is, the probability that at least one of them is pregnant is 1. But it's not certain that at least one of them is pregnant, it could be that all of them are not pregnant. Similarly, if we choose a number uniformly in the interval [0,1], then the probability of choosing 1/3 is 0, but it's possible that we chose 1/3. We cannot ignore that as an impossibility either, otherwise when we chose a number x, we could always claim "it's impossible that we chose exactly x!".