Was curious just how rare an event it is to look up and happen see a perfect ISS pass taking place.

From any given location at my latitude (40 roughly), you get a late evening twilight pass (late enough that the sky is inky blue, early enough ISS is still illumated more or less horizon-to-horizon) at an elevation of 60 degrees or more only two or three times per year, I figure (maybe even 1 or 2). Call it two minutes of peak viewing, and if you make one look up on a random day sometime during the hour of late twilight, that leads to about a 1 in 4000 chance of ISS happening to be there. Somewhat Less if you figure your field of view isn't whole sky. Considerably less if you add in cloud cover, depending on local climate. So call it 1 in 15,000 or so as an approximation.

Roughly a once in a lifetime proposition.

Of course, my walk lasted about 30 minutes, though I didn't necessarily look up in all directions all the time (plus obstructions from trees in many places). And there are many days I'm out for an evening walk, or when I get more quite a few peeps at the evening sky because I'm driving, looking out a window, out running errands, etc. Then again, there are many evenings I'm in my windowless office, in a theater or restaurant, etc. and get zero views of the sky.

Better odds than once in a lifetime, but probably not more than once every decade or so -- and given that ISS has been in orbit for 7.5 years and this was my first good serendipitous pass, I guess that's about right!