I agree with you.

But I don't think "prudent and cautious" can quite be boiled down to just a certainty of outcome. Risk/reward plays in a lot. If we take "cautious" to mean a medium degree of risk aversion, then I don't think a cautious person would risk their year's wage on the chance to double it, even with a 55% certainty of success. However, I think they would risk $10 for a 55% chance of getting $20.

So what is at stake? What's the cost of an invasion of privacy?

Because of civil asset forfeiture, the base value is however much cash happens to be in the car, assuming it's enough to be "suspicious" (how just having cash is suspicious, I don't know). Most people don't have large amounts of cash in their car, but those who do have, well, a large amount.

The other quantifiable loss to a car search is time. Based on a quick search, it seems the average hourly wage of americans is $25. Wage isn't really the best evaluation of time, but it's easy. That covers the time wasted, but not the losses due to being late to something. A car search could make someone miss an appointment, or even get fired — or nothing.

I'm going to estimate that the sum of how much the average person stands to lose to asset forfeiture and time is about $100. That's of course not even considering the emotional impact of having your privacy violated, or the potential non-legal consequences of having a car search, say having an affair exposed. I'll try to give a personal answer to that question. How much would someone have to pay me for me to be okay with them tipping of the police that I have drugs in my car? Well since I'd be able to plan for it, missing appointments and asset forfeiture are hardly a concern, but time is. I suppose someone could hire me to stand around and be bored for an hour for $40. I'd let them tip off the cops for say, $600. Since that's how much it would take to make it worth my while and not really just meet the baseline of acceptable, I'll cut off a bit from that, say $60. And then subtract the $40 for my time. Adding in the estimated tangible cost, and that's $600 again.

So let's go with $600 as the cost of an erroneous search. Now we need the value of a successful search.

It's hard to quantify (I'd argue the value is negative because of the questionable value of the war on drugs and the cost of incarceration), but for this purpose, I'll use bounties. A quick search turned up a really bullshit looking page that mentions a county police department offering $1000 cash to anyone who turns in a heroin dealer. While the value to the county is going to be higher than the bounty they offer, I'm going to assume that since this county is offering a bounty in the first place, they value it slightly higher than other municipalities. So let's go with $1000 as the value of catching a drug dealer.

Risking $600 for a 55% chance of $1000 isn't just not cautious, it's a losing game.

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So what would I consider cautious? Risking $1000 for a 60% chance of doubling it? I'd characterize that as "cautiously optimistic". 65%? Same. 70%? Sure I'll call that "cautious". Obviously different people will have different ideas of what "cautious" means.

But by my definition, and my value estimates, I'll say the certainty required for probable cause for searching a car with drugs is 85%.