It may be my modern person bias speaking, but I feel like the layman concept of "risk" is so inherent to... well, everyday functioning and any kind of strategic decision making. I know how probability theory was discovered, but I was wondering what people before that, as well as people in different parts of the world, used to express useful concepts such as "two in five ships that we send to location X are maraudered by pirates on the way, while it happens to four out of five by using alternative route Y"? Or, for example, were gambling houses "rigged" like modern ones are and how?
This is interesting as the idea of probability in the way you describe it is a very modern invention for several reasons. This is largely due to worldview changes, from a very supernatural worldview to a more natural one. In most societies in history (and probably prehistory too), risk was seen more as a cause or result of pleasing or angering gods, spirits, and other supernatural beings.
This changes as we develop a concept of more natural law and in the history of Cardano and Pascal and others who develop modern probability theory at the same time that a more modern natural law approach develops. Before these thinkers, there is very little evidence of mathematically calculating probability and it's well after Bayes in the late 1700s to early 1800s that we start seeing people use evidence to infer risk mathematically like in your example.
However, you're right about the idea of risk being central to this and in the middle ages, this idea of risk becomes important in maritime insurance. Greek and Roman financiers had loans that would be taken out to protect shipping in a way similar to insurance today and Romans started to base these loans more on the danger of the journey, though it wasn't explicitly mathematical. In the late 1300s, this becomes more mathematically modeled through insurers of shipping in the Mediterranean who have an advantage to start to model how risky it is to insure a shipment.
This also factors in with the development of loans as more of an industry once usury laws become less powerful (mostly middle ages), because the risk of the loan has to be assessed to factor in the interest. This leads to some of the first calculations of risk. In fact, this was used as a justification to deal with usury laws: e.g. Franklin, 2001, p 264), quoting a writer around 1200 "If he commits capital to the fortuitous risk, hoping to receive something over and above it, there is no usury involved, since the risk turns both ways, provided that the contract is made according to the accustomed course of buying and selling.” In this case, the risk was not really modeled but the idea of risk versus no risk was used as a justification for probability.
Source - if you're more interested in this, the whole book is very interesting reading.
James Franklin. (2001). The Science of Conjecture : Evidence and Probability Before Pascal. Johns Hopkins University Press.