According to the meaning of the question, there are seven books on the shelf. Arrange them in a row at random, and there are 77 different arrangements.

If the three books on the left are all math books, the arrangement of these three math books is A33, and the arrangement of the other four books on the right is A44.

Then there is the arrangement of 33×A44, and the three books on the left are all math books.

So the probability that the three books on the left are all math books is P=A33? a44a 77 = 1×2×3× 1×2×3×4 1×2×3×4×5×6×7 = 135；

So the answer is 135.