I don't understand the question; probabilities don't really play directly into random generation. If you mean guaranteeing a consistent set, you can use a seed for your random numbers. The default seed in Java is
(seed ^ 0x5DEECE66DL) & ((1L << 48) - 1), but you can change that to 1 if you want to. That doesn't mean you end up with 1, 2, 3, . . ., but it does mean that if you run two randoms with the same seed it will result in the same numbers.