How did the Jewish view of an afterlife inform the Christo-Islamic view of an afterlife?

According to some of my reading, Many Jews either don't believe in Hell at all and rather prefer to believe in a state of non-existence for the wicked, believe in Hell as a place of punishment called Gehenna (mentioned in the Mishnah in Kiddushin 4.14, Avot 1.5; 5.19, 20, Tosefta t.Bereshith 6.15, and... show more According to some of my reading, Many Jews either don't believe in Hell at all and rather prefer to believe in a state of non-existence for the wicked, believe in Hell as a place of punishment called Gehenna (mentioned in the Mishnah in Kiddushin 4.14, Avot 1.5; 5.19, 20, Tosefta t.Bereshith 6.15, and Babylonian Talmud b.Rosh Hashanah 16b:7a; b.Bereshith 28b), or believe that there is a state known as Sheol in which the unrepentant dead dwell forever in a non-rewarding gloom, but in which they are not punished per se. (Only unrewarded.) Most Jews believe in Olam Haba ("The World to Come") as a heavenly state for both good Jews and righteous gentiles (non-Jews). Still others, particularly the Hasidim, believe in a concept similar to reincarnation called "gilgul", or the transmigration of souls which features in some interpretations of the Kaballah.

So with all these varying beliefs, and the fact that >> most << Jews don't believe in Hell and do believe that both people of their faith and others can enter paradise, how did the Christian and Islamic dichotomies of Heaven and Hell come about? (Although there are a handfull of Christians who don't believe in Hell.)

Judaism and the other two Abrahamic faiths seem worlds apart in this regard.
Update: That is, the Christo-Islamic view being that only their respective religions/followers can lead to salvation and for the rest it is eternal torment.
Update 2: @LightGuardian (first answer down):

You didn't answer my question. You simply repeated what I already stated. I want to know how the Jewish view gave rise to the Christo-Islamic view.
Update 3: Sources please. Sources everybody. Please explain in detail,
4 answers 4