Input-Output Circuit Issue
Try out this schematic. It will work.



So code will be :

int red = 8;
int uv = 9;
int redbutton = 2;
int uvbutton = 3;
int redbutcondition = 0;
int uvbutcondition = 0;

void setup()
{
  pinMode (red, OUTPUT);
  pinMode (uv, OUTPUT);
  pinMode (redbutton, INPUT_PULLUP);
  pinMode (uvbutton, INPUT_PULLUP);
}

void loop()
{
  redbutcondition = digitalRead(redbutton);
  uvbutcondition = digitalRead(uvbutton);

  if (redbutcondition == LOW)
  {
    digitalWrite(red, HIGH);
    digitalWrite(uv, LOW);
  }
  else if(uvbutcondition == LOW)
  {
    digitalWrite(uv, HIGH);
    digitalWrite(red, LOW);
  }
}