You get it as the solution to the equation. In a non-time-travel case, you have a fixed initial state (probability distribution is zero in all but one place), and a slightly spread out distribution for the future (errors are possible, if unlikely). If you perform another computation after that, and want to know what the state of the computer will be after performing two computations, you take the probability distribution after the first computation, transform it according to your computation (with possible errors), and get a third distribution.
All that changes here is that we have a constraint that two of the distributions need to be equal to each other. So, add that constraint, and solve for the distribution that fits the constraints.
You get it as the solution to the equation. In a non-time-travel case, you have a fixed initial state (probability distribution is zero in all but one place), and a slightly spread out distribution for the future (errors are possible, if unlikely). If you perform another computation after that, and want to know what the state of the computer will be after performing two computations, you take the probability distribution after the first computation, transform it according to your computation (with possible errors), and get a third distribution.
All that changes here is that we have a constraint that two of the distributions need to be equal to each other. So, add that constraint, and solve for the distribution that fits the constraints.