I'm not sure that a low-chance coincidence would point to the Christian God specifically, but it may point to some sort of god-concept or "intelligence" that is actively engaging and affecting the world to make certain events more probable than they should be.
Low-chance coincidences happen all the time. A coincidence is basically nothing but a way of looking at things.
Each week a person wins the lottery.
The chance that this particular raindrop hit my nose at this very point in time was probably one in billions of trilliards.
You need to first give significance to the link between two (or more) events to even think of it as a "coincidence".
Think about rolling a die. If you get 50 sixes in a row, you might think something is funny with the die. It's natural, given the coincidence, to assume some sort of intelligent agent is messing with the "natural" probability distribution. In this case, its probably the maker of the die who built it to be weighted to land on 6.
Firstly, "it´s natural" doesn´t mean "it´s reasonable".
Secondly, I already conceded that humans have a tendency to look for significance.
Thirdly, I will also concede that humans have a tendency to assume intention behind a coincidence that strikes them as significant. That doesn´t mean it´s necessarily rational.
Fourthly, there is a difference between assuming intention on part of one of the persons involved and spontaneously inventing a particular entity that you can ascribe the intention to. (Remember, I explicitly stated that I wasn´t talking about believers confirming their already existing beliefs, but about "convincing non-believers").
Now, if, instead of a die, you have an example that is much more complex such that a human intelligence couldn't possibly engineer the coincidence, then maybe there is some other intelligence out there messing with the probability distribution of events.
See my examples above. Highly unlikely coincidences happen so often that we don´t even think of them as "coincidences". Actually, the more complex a system is the more low probability coincidences will happen.
As in madaz's example, the chances that two people from the same street would go to the same park across town at the same time seems quite low.
1. It isn´t any lower than with two particular persons from different streets.
2. Come to think of it (and seeing that we are talking about a well known local public recreational), the chance isn´t even that low. If you go to a public place in your area the chance to meet someone from your street is actually quite high. Higher than to meet, say, a particular person from the other end of the world, anyway.
If you built in some simplifying assumptions, you could nail down a rough estimate of the probability but I don't know if my probability skills can actually do the computation.
I´m not an expert in that field, either. However, it´s safe to say that meeting a person from your street at a public recreational area in your neck of the woods is doesn´t have a lower probability than meeting someone there whom we have randomly picked from a list of the inhabitants of the world. Thus, what actually strikes us as significant isn´t the low probability.
Could be aliens
I dunno.
Personally, if I were to look not only for significance but also for an intentional force, I would first go with the persons involved. Before I would assume Gods, fairies, aliens I certainly would consider the possibility that the woman is following me around, for whatever reason.
On another note, even if I came to the point of assuming supernatural or other exceptional intentions, I would need them to make some sense. At this point, I have no idea what God´s purpose might possibly be in having two people from the same street meet at a recreational area. An attempt at recruiting believers?
