The chance is so little that the calculator cannot handle it....

The last evening of our vacation in Athens. Sitting with family on their balcony glazing out in all the high storied buildings made of Concrete. Everyone is sleeping except another family in the opposite concrete building also at their balcony. Nothing strange about that. Before I continue I would like you to think about how many inhabitants Athens has (around 3,8 millions) and then how many seats an aeroplane has (150-200 seats). Have you done that now? OK let us continue...next morning at the Athens International Airport we are checking in and to our BIG surprise our balcony neighbours are also checking in on the same flight back to Stockholm. I REALLY tried to calculate what the chance of this was on the calculator but failed. Can anyone calculate what the probability in percentage is of this occurrence?   It must be pretty slim....actually the calculation said 0,1%. I have not figured it out what the chance is that we are living at the same street yet...but it must be pretty rare...