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 ʻalayhi wa sallam, is His slave and Messenger.
If jumping out the third floor window would cause certain death, then this person should not jump but rather stay where he is, perhaps Allaah would send someone to put out the fire. However, if burning to death is certain while jumping out the window would not necessarily cause death, then he should jump out the window to save himself from the burning fire. If death is certain in both cases, then he should stay where he is and not jump to a certain death. This is in adherence with the Fiqhi rules: “Harm should not be eliminated by like harm,” and “The more severe harm is removed by committing the lesser harm”.
Al-Musawwadah fi Usool Al-Fiqh reads, “Jurists (scholars of Fiqh) held that if a ship is on fire and the person on board knew that he would most likely survive the fire if he stayed on board or would most likely survive by jumping into the water, then he is obliged to do what would save his life. If he predominantly thinks that by doing either of them, he will save himself, then he may choose between them. However, if he knew that he would most likely die in either case, then he should stay on board and not take an action that would kill him.” [p. 87]
Allaah knows best.