I am only talking about divine intervention from God, so let's discuss that...
I believe that everyone has free will. We make our own choices and deal with the consequences; good or bad.
What many do not understand is that the choices your ancestors made could affect you today, or your future bloodline. If they did something that caused a genetic mutation (think having children with someone too closely related) then your genes could have a dormant mutation that could pop up on down the line.
Then there is the criminal element of society. They too have free will. If they choose to commit a crime against a person, God does not intervene, otherwise it is no longer the free will of the criminal even though they are causing harm, the death or loss of property to someone else.
That's not to say that God is not saddened by events that take place (maybe God is...who knows) but not intervening is the ultimate conviction in order to allow for free will to take its course.
Edit:
Why are people murdered? Because someone chooses to commit murder.
Why are women raped? Because someone chooses to commit rape.
Why are items stolen? Because someone chooses to steal.
Why are children abused? Because someone chooses to abuse them.
Why do people develop cancer? Because they did something that can cause cancer (smoking, drinking, etc.) or they have some type of genetic mutation in their DNA.
Why have several children drowned at sea (think Syrian refugees)? Because an adult chooses to place them on a boat knowing that the boat could sink.
Why did someone die in a traffic collision? Because someone else was DUI, or speeding, or playing Pokemon Go. Or perhaps the deceased failed to maintain their vehicle and a tire blew out.
The question then becomes, why believe in God if there is no divine intervention, scientific proof of God's existence or anything else to support your views? The answer is...because I choose to.