It is not at all clear that it is possible in reality to randomly select a real number without a process that can make an infinite number of choices in finite time. Similarly, any reasoning about Turing machines has to acknowledge that no real, physical system actually instantiates one in the sense of having an infinite tape and never making an error. We can approach/​approximate these examples, but that just means we end up with probabilities that are small-but-finite, not 0 or 1
It is not at all clear that it is possible in reality to randomly select a real number without a process that can make an infinite number of choices in finite time. Similarly, any reasoning about Turing machines has to acknowledge that no real, physical system actually instantiates one in the sense of having an infinite tape and never making an error. We can approach/​approximate these examples, but that just means we end up with probabilities that are small-but-finite, not 0 or 1