Digital Comparator with ATTiny85 doesn't behave as expected
You have to assign the status of all output pins in each of your "if statement" conditions. Think of it like 'if that happens, I want x, y, &amp; z to be ON, and a, b, &amp; c to be Off'. Unchanging the HIGH status of one output will remain that output HIGH for all conditions. Output pins never change their statuses untill they have an order "your code" to do this. Also you have to replace your code inside a loop function to repeat your code without the need to manually reset your ATTiny.

Assuming LED1 = pinOut1, LED2 = pinOut2, LED3 = pinOut3.
You have to replace "if conditions" in your code by the following:

while( 1 ){
    int a = digitalRead(PinA);
    int b = digitalRead(PinB);

    if ( a == b ) {
        digitalwrite (pinOut1 , HIGH);
        digitalwrite(pinOut2,LOW) ;
        digitalwrite (pinOut3, LOW);
    }
    else if ( a == HIGH ) {
        digitalwrite(pinOut2,HIGH) ;
        digitalwrite(pinOut1,LOW) ;
        digitalwrite(pinOut3,LOW);
    }
    else if ( b == HIGH ) {
        digitalwrite(pinOut3,HIGH) ;
        digitalwrite(pinOut1,LOW) ;
    digitalwrite(pinOut2,LOW);
    }
}


Also according to your application speed requirements, you can add a delay of about 300 ms before reading your digital inputs to allow the user to change the status of these digital inputs.