```ts
/** a divided by b, handling division by zero and non-finite numbers. */
export function safeDivide(a: number, b: number): number {
  if (typeof a !== 'number' || typeof b !== 'number') {
    throw new Error('Both arguments must be numbers');
  }
  if (!isFinite(a) || !isFinite(b)) {
    throw new Error('Both arguments must be finite numbers');
  }
  if (b === 0) {
    throw new Error('Division by zero is not allowed');
  }
  return a / b;
}

function isFinite(value): boolean {
  return typeof value === 'number' && !isNaN(value);
}
```