Suppose you had a random number generator that was capable of generating real numbers of infinite precision (this would be something better than current computer PRNG's, which can only produce numbers of fixed precision, and aren't really truly random). What is the probability of this RNG generating an integer-like number (something like 24.0)? The number of integers and real numbers that can be generated are both infinite, but intuitively, the infinity of integers should be "smaller" than the infinity of real numbers.