FIRST BORN Although the Arabian legislator followed the Mosaic law in so many of his legal enactments, he has carefully avoided any legislation as to the rights of primogeniture although it formed such a marked feature in the Pentateuch, in which the first born of man and beast were devoted to God and were redeemed with a price. In the Muslim law of inheritance all the sons share equally, which in the Mosaic law the eldest son received a double portion of the father’s inheritance. (Deut. xxi 17)
In cases of chiefship, or monarchy the eldest son usually inherits, but it rests entirely upon his fitness for the position. Very often the eldest son is passed by and a younger brother selected as ruler. This was also the case amongst the Jews when Solomon succeeded his father in the kingdom (1 Kings I 30, ii 22)
The curious fact that Muhammad made no provision for these rights of primogeniture may have arisen from his having had no son to survive him.

Based on Hughes, Dictionary of Islam