Coincidence, time, prophecy and the fates
I think that one idea of relevance to this is Jung's idea of synchronicity, which he developed in response to his own premonitions. However, he does suggest that it is about seeing patterns in things rather than about causality outrightly. But, some other thinkers have developed this idea a little differently, as for example, Deepak Chopra in, 'Synchrodestiny'. It is a question of whether what happens in life is mere chance?
Personally, I have wondered about this issue a lot because I had a number of really horrible premonitions as a teenager, especially of people dying and, then they died shortly after. This included my headmaster and several other people I only knew by sight. In one instance, I remember being in the school library and seeing a boy whose name I didn't know and the thought coming through my head, 'he has not got as many problems as me but his dad is going to die.' About a week later, I found out that his father really had died. My various experiences almost made me become unwell mentally because I began to wonder if it was my fault that the people were dying. But, fortunately, I found Jung's autobiography and read about his struggle to understand his premonitions. I have experienced some strange premonitions in adulthood but not to the extent as I did during adolescence.
As for coincidence, personally, I am not convinced that anything in life is pure chance. Of course, it all comes down to a question of meanings but I think that meaning is so central to life that it affects what becomes manifest in the events within our lives.