An opportunity gets its probability from its stage. Each opportunity stage has a probability, and when a user picks a stage, the opportunity takes that stage's probability.
To let users set their own probability, the Administrator has to activate it by clicking Settings → CRM → Fields → Order & opportunities. Under Default fields, turn on Active for Probability:
Users can then choose their own probability of an opportunity by entering a value from 0 to 100 in the Probability field:
Choosing a different stage afterwards replaces the entered value with the new stage's probability. The Probability field is not shown on orders or on opportunities in a 0% or 100% stage.