In general, Western culture is deeply post-Christian. It is the product of the Enlightenment, which introduced into European culture the leaven of se… - William Lane Craig

Therefore, when a person refuses to come to Christ it is never just because of lack of evidence or because of intellectual difficulties: at root, he refuses to come because he willingly ignores and rejects the drawing of God's Spirit on his heart. No one in the final analysis really fails to become a Christian because of lack of arguments; he fails to become a Christian because he loves darkness rather than light and wants nothing to do with God.

Okay, look at it this way: if the evening news has a very high probability of being accurate, then it's highly improbable that they would inaccurately report the numbers chosen in the lottery. That counterbalances any improbability in the choosing of those numbers, so you're quite rational to believe in this highly improbable event.

There is one important aspect of my answer that I would change, however. I have come to appreciate as a result of a closer reading of the biblical text that God’s command to Israel was not primarily to exterminate the Canaanites but to drive them out of the land. It was the land that was (and remains today!) paramount in the minds of these Ancient Near Eastern peoples. The Canaanite tribal kingdoms which occupied the land were to be destroyed as nation states, not as individuals. The judgment of God upon these tribal groups, which had become so incredibly debauched by that time, is that they were being divested of their land. Canaan was being given over to Israel, whom God had now brought out of Egypt. If the Canaanite tribes, seeing the armies of Israel, had simply chosen to flee, no one would have been killed at all. There was no command to pursue and hunt down the Canaanite peoples.
It is therefore completely misleading to characterize God’s command to Israel as a command to commit genocide. Rather it was first and foremost a command to drive the tribes out of the land and to occupy it. Only those who remained behind were to be utterly exterminated. There may have been no non-combatants killed at all. That makes sense of why there is no record of the killing of women and children, such as I had vividly imagined. Such scenes may have never taken place, since it was the soldiers who remained to fight. It is also why there were plenty of Canaanite people around after the conquest of the land, as the biblical record attests.