Pompey is said to have made clients out of entire kingdoms during his campaigns in the East after defeating Mithridates. If Pompey's power base was so large in the East, why would he choose to flee to Egypt after losing to Caesar at Pharsalus? Why not Syria or the Province of Asia? Since Egypt was still technically independent from Rome and I have never heard it mentioned that Ptolemy XIII owed his position to Pompey, I am assuming that Pompey had much stronger hopes of asylum and much stronger bases of power to reorganize resistance from elsewhere in the East.
Egypt was a client state of Pompey's. During his proconsulship of Syria Gabinius, one of Pompey's most important partisans who had sat as consul with Caesar's partisan and father-in-law Piso, was sent by Pompey illegally into Egypt to restore Ptolemy XII to the throne. Gabinius was prosecuted for leaving his province and fighting an illegal war, but Pompey bribed his way to an acquittal. The client status was maintained under Ptolemy XIII and his co-regent Cleopatra--Ptolemy and Cleopatra sent a contingent of the Gabiniani, troops that Gabinius had left behind on garrison duty, to Pharsalus, and Appian reports a force of sixty ships were provided by the two as well. There was every reason to believe that Ptolemy, despite fighting a civil war with Cleopatra at the time, would continue to support Pompey, who almost certainly did not plan to stay for long. Egypt was vastly wealthier than even Syria, and--now this is important--Pompey couldn't have stopped in Syria in any case. Caesar says that Pompey intended to take refuge in Syria, but when he was at Cyprus he received word that Antioch had taken up arms and threatened to kill any Pompeian who tried to flee to the city--Caesar reports that the same thing happened to Lentulus, who was refused access to Rhodes or the harbor when he tried to flee there. Caesar says that at this point Pompey scrapped his plan to go to Syria and fled to Egypt instead. Appian reports that Pompey attempted to flee to Parthia, but was warned against it on the grounds that Crassus' Parthian expedition hadn't exactly endeared the king towards the Romans, so he went to Egypt instead, where the king was still a child and where Pompey was still patron. One wonders whether Syria would've been a reasonable refuge anyway, since Appian reports that Cleopatra was mustering her troops there in preparation for an assault on Alexandria.