Notice, and what each level of it keeps
What the house keeps when a booking is called off depends on the notice in your message and on nothing else, and it never amounts to damages.
Calling an evening off never leaves you owing damages. The only figure in play is the share of the fee already earned by the time your message lands, and the notice you give is what sets it. Three steps, no discretion in them.
The three steps
More than twenty-four hours before the booked hour: nothing is kept, and the front half returns in full. Inside the final day, with her journey not yet begun: half of what you sent stays and half comes back. Once she has set out: what you sent stays whole. Nothing is added on top of it at any step, and no second sum is ever asked for afterwards.
The two reductions
Even the last step yields in two cases. If the evening you released is taken by another client, the money returns in full, because the time was not lost after all. And if you can show that the loss to the house was smaller than the share it held, only the smaller sum stays. Both of those are worth raising in the thread rather than assuming.
The booking with nothing behind it
A returning client's same day hour or two at a city address has no front half, so the scale has nothing to act on. Dropped before she leaves, it costs nothing. Dropped once she is on her way, it costs the share of the fee that her journey represents and no more than that. A move of date, meanwhile, is a separate thing from a cancellation, and the one free move explains where the two meet.