When a Parsi dies leaving neither lineal descendants nor a widow or widower nor a widow or widower of any lineal descendant, his or her next-of-kin, in the order set forth in Part II of Schedule II, shall be entitled to succeed to the whole of the property of which he or she dies intestate. The next-of-kin standing first in Part II of that Schedule shall be preferred to those standing second, the second to the third, and so on in succession, provided that the property shall be so distributed that each male and female standing in the same degree of propinquity shall receive equal shares.