It is a great question and the same one that needs to be asked regarding the Holocaust and all sorts of horrors and sinful things that have happened and have kept happening to relatively innocent people throughout history. It is a question that has plagued me most of my life.
Fundamentally, evil exists because men have chosen to commit evil continuously (Genesis 6:5; Jeremiah 17:9; Mark 7:21-23; Matthew 15:19).
Additionally, as fallen beings and due to the fallen creation that we live in, (which we caused to fall), the demonic realm has been empowered to tempt and otherwise drive people to do even more wickedness. (Exhibit A, B, C, D and E - Mao Zedong, Adolph Hitler, Pol Pot, Idi Amin, Isis, et al.)
God has brought a remedy to all of this by sending His Son to pay the penalty for our sins by dying on the Cross and taking them upon Himself. However, most of mankind continues to reject that solution and continue in their wickedness (John 3:16-21). In essence, evil men continue to do evil because they have rejected Christ and His solution to the problem. If they did accept Him as their solution, He would send them the Holy Spirit to guide them through a sanctification process that eventually will cause them to hate evil and cling to what is good (John 14:15-17; 15:26; 16:7-15; Romans 12:9).
So, in short, such evils exist because men reject God and choose to continue in them.
It is not God's fault! It is our fault, whether we personally commit the more grievous evils or not. God is innocent of all charges - even the one of not doing anything to stop sinful acts - though He will stop them upon His return, after all men have been given the chance to choose the source of good or the source of evil.
The Bible teaches that without taking advantage of God's remedy for sin, "evil men and imposters will go from bad to worse deceiving and being deceived" (2 Timothy 3:13).
It seems that the only way that sinful man can recognize his need for a Savior is to see the consequences of sin all around him and cry out for God to send one. Sadly, most won't do that. (Even when God did send a Savior - Jesus Christ - most men refused to accept Him).
Concerning innocent victims of sin, I asked God one night to explain why He allows them to suffer. His reply to me was, "What you're really asking Me is how could I love you and allow you to suffer." I replied, "Yeah God, now that you mention it, that is what I am asking!" He replied, "I have already proven My love for you by dying a horrific death on the Cross. And when the Cross becomes enough proof for you that I love you, then you will find the peace that you are seeking."