Map angles to a 0-1 range

Let's say you have two angles, and you label them 0 and 1. Then you have another angle x. You also know if you'll be going Clockwise or Counter Clockwise to get from angle 0 to angle 1. How do you calculate a number that can describe that third angle?

Examples:

Angle at 0	Angle at 1	Rotation Direction	Target Angle	Mapped number (x)
0°	90°	CCW	60°	2/3
90°	0°	CW	60°	1/3
0°	180°	CW	90°	1.5
0°	180°	CCW	90°	0.5

Problems I'm having:

When x can't be supported within 0 and 1 (I am fine with it just telling me it couldn't do it, but having the number would be cooler).
When switching from Counter-Clock-Wise (CCW) to CW.

Solution

Check the next approach:

def ratio(x, a, b, dircw = False):
    if dircw:
        if x > a:
            x -= 360
        if b > a:
            b -= 360
    else:
        if b < a:
            b += 360
        if x < a:
            x += 360

    return (x-a)/(b-a)


print(ratio(60, 0, 90))
print(ratio(60, 0, 90, True))
print(ratio(60, 90, 0, True))
print(ratio(90, 0, 180, True))
print(ratio(90, 0, 180))

0.6666666666666666
1.1111111111111112
0.3333333333333333
1.5
0.5

We consider solution of linear equation (solve inverse of linear interpolation)

x = a*(1-t) + b*t

for unknown t.

We have to make normalization to provide b after a in cyclic manner in both directions - so b+- correction.

To get only positive results, we normalize also x.