We are talking about the case when the first strike HAS happened. So the probability of the two strikes has now collapsed to 1000:1.
Needless to say, we don't disagree about the mathematics of the probabilities - and I perhaps confused matters by introducing a probabilistic discussion in relation to a common idiomatic figure of speech ("lightning doesn't strike the same place twice").
Since I was talking about (per 'the phrase') was "lighting striking the same place twice", what I was saying was literally correct - i.e. if everything is random, then the probability of "lighting striking the same place twice" is, indeed, the square of the probability of one strike (i.e. 1:1,000,000 if the probability of one strike is 1:1000). In other words, I was not, at that point, talking about a situation in which one strike had already occurred - and that's probably what has confused things a bit.
The point I was trying to make was not really a mathematical one at all. My point was that (assuming everything is random) the fact that one has been incredibly unlucky in having already suffered from one lightning strike is not really a reason to worry further about "it happening again", since the probability of that happening is as incredibly small as was the probability of the first one having happened in the first place.
This rather illustrates a common problem with the practical interpretation (in relation to an individual person, building or whatever) of extremely small probabilities of discrete events. When such probabilities are larger, meaningful interpretation is much easier. . If, for example, the probability of something happening in any one year is, say, 0.10 (10%, 1:10), then one can say that the most likely number of occurrences of that event during a 50 year period (say, an 'adult lifetime') would be 5 - or if the probability were 1:25, then the most likely number of occurrences of the event in 50 years would be 2 etc. etc. One can base decisions on such information.
If the probability were 1:1,000, then by far the most likely number of occurrences of the event in 50 years would be zero. However, 'by far the most likely number of occurrences of the event in 50 years' would again be zero for any probability less than 1:1,000. Hence, 'by far the most likely number of events in 50 years' (which is what matters to an individual person/building/whatever) will be the zero whether the probability per year is 0.001 (1:1,000), 0.00001, 0.000000001 or whatever.
What matters in terms of the individual (person/building etc.) is the number (if any) of discrete events which they are likely to experience in a given time period (e.g. 'a lifetime') - an 'average number of expected events (for the person/building etc.) in 50 years' (which is easily calculated) is not really a very useful guide to anything.
For reference, the following indicates the probability of various numbers of events occurring in 50 years for a range of probabilities of the event occurring in a particular location in any one year. As you can see, even with a 1:1,000 probability per location per year (obviously very high for lightning strikes), there is still a 95% chance that one will suffer no strikes in 50 years - and when one moves to probabilities more realistic for lightning strikes, the probability of there being anything more than zero events in 50 years gets so small as to probably not be worth thinking/worrying about (regardless of whether or not any previous strikes have occurred)!
Kind Regards, John