According to Pavic, what did the Khazars do as a result of the Khazar polemic?

According to legend—on which the Dictionary of the Khazars is based—the Khazars were a Turkic tribe who purportedly vanished during the tenth century AD. In the story, the ruler of the Khazars invites a rabbi, a monk, and a dervish to interpret a portentous dream. The three holy men stage a polemic, or debate, between them, hoping that their individual interpretation of the dream will be the one to prevail. The religion of the debate's winner—Christian, Jewish, or Muslim—will be the one that the Khazars will adopt.
However, Pavic, in his creative reconstruction of the lost dictionary of the Khazars, does not tell us who actually wins the debate, or which religion the Khazars chose to adopt as a consequence. All we know is that the Khazars chose en masse to convert to one religion, and that they soon vanished from history not long afterwards.