<select  name="conductor" id="conductor" class="form-control">
<option value="">Seleccione...</option>
<?php
$query1="SELECT  * FROM conductor";
$result1=mysqli_query($con, $query1) or die (mysqli_error());
while ($row=mysqli_fetch_array($result1)){
echo '<option value="'.$row['id_conductor'].'">'.$row['nombre'].'</option>';
}
?>
</select>

function pdf(){
conductor =$("conductor").val();
$.ajax({
url:"cartaresponsiva.php",
type: "POST",
data: {condutor: conductor},
success: function(respuesta){
}
});
}

<table border='0' cellspacing='0' cellpadding='0'>
        <thead>
          <tr>
            <th class="no">#</th>
            <th class="desc">Nombre</th>
            <th class="unit">Vehículo</th>
            <th class="qty">Fecha de Reasignación</th>
          </tr>
        </thead>

 <tbody>
  <tr>
  <td class="no"></td>
  <td class="desc"></td>
  <td class="unit"></td>
   <td class="qty"></td>
  </tr>
  </tbody>

  <tfoot>
  <tr>
  <td colspan="2"></td>
  <td colspan="2">Control de Flotilla</td>
  </tr>
  </tfoot>
</table>