probability function
Binary probability at strike for the given side ('up' = P(>strike),
'down' = 1 − up).
Implementation
double probability(PricerInputs inputs, double strike, String side) {
// Anything not exactly 'up'/'down' must throw rather than silently price
// the DOWN side: `side` arrives from UI state, JSON, or a DB column at
// runtime, where a type alone does not protect (same guard as
// `binaryRangeTicks`).
if (side != 'up' && side != 'down') {
throw PredictInputError("side must be 'up' or 'down', got '$side'");
}
final up = upProbability(inputs, strike);
return side == 'up' ? up : 1 - up;
}