According to the histogram of frequency distribution, there are no students with grades below 60, so the number of students with grades below [40,70] is the number of students with grades below [60,70], and the frequency of students with grades below [60,70] is 0.03x10 = 0.3.

There are 120 students whose grades are within [40,70], so the total number of students in this school is 1200.3 = 400.

So there are 400 senior three liberal arts students in this school.

So the answer is 400.