It should be very helpful to know if a scroll bar within a scroll pane is visible or not.
In my case, I want to add 1 pixel gap between the scroll pane content and the scroll bar (See attached screen shot).
To do this, I need to dynamically add/remove css rules :

.scrollBarVisible {
    /* Add 1 pixel gap between the ScrollPane content and the ScrollPane scroll bar when the scroll bar is visible */
    -fx-padding: 0 1 0 0;
}

.scrollBarNotVisible {
    /* Remove 1 pixel gap between the ScrollPane content and the ScrollPane scroll bar when the scroll bar is _not_ visible */
    -fx-padding: 0;
}

A pseudo-calss would allow something like :
.scroll-bar {
    -fx-padding: 0;
}
.scroll-bar:visible {
    -fx-padding: 0 1 0 0;
}