All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
The basic rule concerning the property of a Muslim person is that he has obtained it legally, and it is not due on anyone to delve into investigating its origin, otherwise, it will be a kind of dispraised Tanattu’ (excessive contention).
Shaykh-ul-Islam Ibn Taymiyyah said: “As for the Muslim whose condition is unknown, then there should be no doubt, in principle, about (the permissibility of) dealing with him; and whoever refrains from dealing with him out of extreme piety, he has indeed made a religious innovation for which Allaah has not sent down any authority.”
Hence, as long as you received this ticket as a gift from your colleague and used it to enter the draw, and you won the car, then there is no harm if you benefit from the price of the car, as the basic rule is that your colleague obtained the ticket legally.
The fact that the organizing charity is non-Muslim neither affects the ruling nor forbids benefitting from the prize, because it is permissible to accept and benefit from the non-Muslim's gift, in accordance with Allaah's Saying (what means): {Allaah does not forbid you from those who do not fight you because of religion and do not expel you from your homes - from being righteous toward them and acting justly toward them. Indeed, Allaah loves those who act justly.}[Quran 60:8] Also, it is narrated by Ahmad that the Prophet, sallallaahu ‘alayhi wa sallam, was invited by a Jew to a meal of barley bread and rancid fat, and he, sallallaahu ‘alayhi wa sallam, accepted the invitation.
Allaah Knows best.