What price injustice? How can you ever justify deliberately hurting an innocent person, however bad the consequences of not doing so?

Countries only have finite budgets, that have to be split between health, railroad safety, the justice system, and many other things. No country can afford to give every citizen the best health care that money can buy. There comes a point where you reach diminishing returns. Where you say, "I have an additional $1,000,000. If I put it into heath, I will on average save just 1 more life. If I put it into railway safety, I will on average save 10 more lives.". Similarly with the justice system. There is only so much money you can spend on additional safe guards for the innocent. Sooner or later you reach a point where you say "I know that this policy, if implemented, will on average harm 5 innocent people a year. But to reduce that to 4 a year would cost an extra $15, 000, 000 which is better spent elsewhere."

From a Precedent Utilitarian perspective, every society places a large but not infinite value on protecting the innocent, and this is just another factor to take into account, like the chance of being struck by lightning.