How is minimum infectious dose defined?
Minimum infective dose is the minimum number of infectious particles that causes infection/illness in 50% of those given that dose.

Practically this is only really measurable in a controlled laboratory setting, but one can estimate it for real world circumstances as well.

It isn't easy to know how exactly the probability will vary around the MID - there are too many factors related both to the individual and the pathogen to make simplistic assumptions (like assuming each individual infectious particle has an independent probability of leading to infection). It is typical that higher initial exposure (particularly for foodborne illness, but seems to be an issue with SARS-CoV-2 and other respiratory viruses as well) leads to more severe illness, however.