If all probabilities have to sum to 100% at all times, it limits how you can go from one state to another. I think an additional fact you’re unaware of here is that states transition into each other smoothly. So if you’re at 80% state A and 20% state B, at a very small time later, you can only be at 79% A and 21% B, say. This is related to the fact that the time evolution operator can be written as a power series in dt.