¿Cómo crear 3 listas desplegables dependientes usando PHP ajax JQUERY?

Pruebe la siguiente implementación pura de JS -

var stateObject = {
  "Three Wheelers": {
    "Bajaj": ["Bajaj RE CNG", "Bajaj Diesel"],
    "Atul": ["Piaggo", "Shakti"]
  },
  "Two Wheelers": {
    "Hero": ["Splendor", "CBZ"],
    "Honda": ["Hornet", "CBR"],
  },
  "Car": {
    "Suzuki": ["Swift", "Ciaz", "Baleno", "Dzire", "Brezaa", "Ertiga", "Celerio", "Eco", "Omni", "Alto", "Scross", "Ignis", "WagonR"],
    "Hyundai": ["i20", "i10", "Creat", "Eon", "Xcent", "Santro", "Tucson", "Elatrna"],
    "Volkswagon": ["Jetta", "Polo", "Passata", "Polo", "Tiguan", "Ameo"],
    "Nissan": ["Terrano", "Duster", "Micra", "Sunny"],
    "Honda": ["City", "Verna", "CR-V", "Accord", "BR-V", "Brio", "Amaze", "Jazz"],
    "Ford": ["EcoSports", "Endaviour", "Figo", "Freestyle", "Aspire"],
  }

}
window.onload = function() {
  var stateSel = document.getElementById("stateSel"),
    countySel = document.getElementById("countySel"),
    citySel = document.getElementById("citySel");
  for (var state in stateObject) {
    stateSel.options[stateSel.options.length] = new Option(state, state);
  }
  stateSel.onchange = function() {
    countySel.length = 1; // remove all options bar first
    citySel.length = 1; // remove all options bar first
    if (this.selectedIndex < 1) {
      countySel.options[0].text = "Select Brand"
      citySel.options[0].text = "Select Modal"
      return; // done   
    }
    countySel.options[0].text = "Select Brand"
    for (var county in stateObject[this.value]) {
      countySel.options[countySel.options.length] = new Option(county, county);
    }
    if (countySel.options.length == 2) {
      countySel.selectedIndex = 1;
      countySel.onchange();
    }

  }
  stateSel.onchange(); // reset in case page is reloaded
  countySel.onchange = function() {
    citySel.length = 1; // remove all options bar first
    if (this.selectedIndex < 1) {
      citySel.options[0].text = "Please Modal"
      return; // done   
    }
    citySel.options[0].text = "Please Modal"

    var cities = stateObject[stateSel.value][this.value];
    for (var i = 0; i < cities.length; i++) {
      citySel.options[citySel.options.length] = new Option(cities[i], cities[i]);
    }
    if (citySel.options.length == 2) {
      citySel.selectedIndex = 1;
      citySel.onchange();
    }

  }
}

<select id="stateSel" size="1" name="vehicle_type" class="form-control input" required>
  <option value="" selected="selected">Select Vehicle</option>
</select>
<br>
<br>
<select id="countySel" size="1" name="brand" class="form-control input" required>
  <option value="" selected="selected">Select Brand</option>
</select>
<br>
<br>
<select id="citySel" size="1" name="modal" class="form-control input" required>
  <option value="">Select Modal</option>
</select>