I've done some exercises to visualize various patterns of event distribution to understand how the Jones probability works. For this I worked with an 18 day sequence with 9 quakes in various distributions, and a 3 day prediction window.

To start, only 1 quake per day, equally spaced: 010101010101010101
Broken into consecutive 3 day windows: 010 101 010 101 010 101
Number of windows with hits: 6
Total number of windows: 6
Probability of any one window being a hit: 6/6 = 1.0

Next, let's group all those 9 quakes in a row: 111111111000000000
Broken into consecutive 3 day windows: 111 111 111 000 000 000
Number of windows with hits: 3
Total number of windows: 6
Probability of any one window being a hit: 3/6 = 0.5

And now, put all the quakes into one day: 900000000000000000
Broken into consecutive 3 day windows: 900 000 000 000 000 000
Number of windows with hits: 1
Total number of windows: 6
Probability of any one window being a hit: 1/6 = 0.167

Even though intuitively it may seem that 9 quakes across 18 days should always give a probability of 9/18 = 0.5, the Jones method gives different results depending on the actual distribution.

It makes sense when you look instead at the windows and not the actual quakes. When you do that, the above three patterns become, respectively:
111111 - 111000 - 100000

So visualizing it this way, it's immediately obvious that the odds of a hit for any 1 window does indeed depend on the distribution of the quakes.

What we can tell from this is that because quakes do tend to cluster in time, particularly due to aftershocks, the odds of a hit are much lower than one would think.

The only caveat to all this is that this probability calculation is dependent on the historical record - the pattern of past quakes. I'm reminded of the disclaimer on investment claims, "past performance is not indicative of future gains." Fortunately, we have no reason to expect that the statistical temporal distribution of quakes in the immediate future will be any different than it has been in the recent past.

Brian