Yeah, see, you can't do that. You're trying to change your model from inside your model; you're basically saying, "If the probability of success is 97%, and this launch was a success, what is the probability the next launch is a success?" The answer has to be 97%, because inside your model, the two launches are independent events.

You have to go meta: Instead of asking "What are the chances the next launch will succeed?" you ask, "What are the chances that my model, which predicted this launch would succeed with a probability of 97%, is correct?" To do that, you need a prior probability that the model is right, and you need other possible models. More complicated to do with this than the mammogram example, because you either have cancer or you don't, but in this example, the probability of success can be anywhere between 0 and 100%.