Sister I didn't know about with the same birthday!

My father passed away on the 2.2.2002 at 2.00pm at the age of 66. The day after he died we were going through his briefcase which he had always kept locked. My mother, brother and I found a number of birthday/christmas cards from someone calling him "Daddy". In June 2003 (the following year) a 22 year old girl called Jane managed to track down my brother via the internet, who had previously been in an 80'sboy band, and she confirmed we had a half sister. When we got talking, she told me her birthday was 6th March, exactly the same day as mine! My father had been living a parallel life, and had had another daughter on my 16th Birthday. We soon met up with my half sister, and have now become very close. She had always known about us, my Dad had told her she had a famous brother, and a sister, that one day he would take her to meet us, and that he was separated from his wife, my mum. My Mum and Jane's Mum have also met now, and any animosities have been buried. My Dad unfortunately is no longer with us to defend himself! But we are all sure he is up there somewhere looking down on us and is happy that we have all finally met! And the chances of my sister and I being born on the same day, in two parallel lives? We feel it is a huge coincidence, and when we tell people the story they often say it brings them out in goosebumps!