The gemara quotes a machlokes Tanaim as to what the navi meant by “tzom ha’asiri,” the fast of the 10th month. We pasken that it refers to the 10th day of the 10th month when the siege was laid around Yerushalayim; however, there is another view that holds it refers to the 5th day of the 10th month when the news of the churban reached the golah.
I understand why you have to fast when something bad happens or on the anniversary of something bad happening. We fast 9 Av for the churban. But why should there be another fast when you get the news about something that happened months ago?
It seems that in Chazal's eyes hearing about tzaros is itself a tzarah worth fasting for. There is a reason the Mishna in Brachos uses the term “besoros tovos” for good news but “shemu’os” – not “besoros” – “ra’os” for bad news. A besorah means tell your friends.; a shem’ua is something you happen to hear about. Bad news is not something you want to spread or want to hear. I don’t know what Chazal would make of 24x7 cable and all kinds of other media that bring every detail of every tzarah in the world to a person’s doorstep or computer screen. We've lost that degree of sensitivity.