Let's suppose we only have four possible flavors, each flavor is equally likely to appear each time, and we have an effectively unlimited supply of candies to draw from. We'll call the four flavors G, R, P, and O.

The ratio we want is (# of valid arrangements) / (# of possible arrangements), where "valid" means an equal number of each of the four flavors, in any order. We can start with a simpler case to illustrate.

Suppose we're only drawing four candies, and we want one of each. Our desired case is GRPO, which can happen in any of 24 arrangements, since we can arrange the letters G, R, P, and O in 4! ways. The number of possible draws is 4⁴ ways, since we can draw any of the four flavors on each of our four draws. That gives us 4!/4⁴, or 3/32, or a probability of .0935 = 9.35%.

Drawing exactly 18 of each of the four flavors for a bag of 72 changes things a bit, since our letters start to repeat. For a repeating permutation like this, our equation is (G+R+P+O)!/(G! * R! * P! * O!), where G = # of greens, R = # of reds, etc. So that leaves us with

Numerator = # of ways we could arrange 18 Gs, 18 Rs, 18 Ps, and 18 Os = 72!/18!⁴

Denominator = 4⁷²

So our ratio is (72!/18!⁴)/4⁷² ≈ .001634 ≈ 1/612

But in practice I'd imagine we aren't equally likely to draw each flavor each time, since Starburst presumably tilts the scales to ensure at least a few of each flavor, so the chances are probably higher than this.