Hamas is not, and never was a majority in Palestine. It's trending upward since mid-november (what's happening in the West Bank might be the reason why).
Check the election stats, Hamas "won" but without any clear majority.
Moreover they won on the promise that they would seek a peaceful resolution with Isreal and they were (at that time) clearly the better of the only two realistic choices.
I’ve done some research. In fact, Hamas won 74 seats out of 132 [1] and, hence, acquired a convenient house majority. Assignment of seats were done by applying a mixed proportional and majority rule (similar to how it works in FRG), that’s why their voter share of 44% translated into more then twice the amount of seats. But, nevertheless, Hamas won the elections even by voter share alone. However, governance in Palestine is split between president and parliament. Since Fatah did not want to grant power to Hamas, president Abbas did not cooperate in the aftermath of the elections eventually resulting in a civil war and an ejection (and murder) of Fatah supporters establishing Hamas‘ one-party governance of Gaza. Israel’s sanctions came into effect after Hamas failed to renounce violence against Israel and its citizens.
(BTW: The elections were held in January 2006 — not in 2007 as I have stated above.)