Android : Refresh data in a Android's ListView after webservice called?

Here is what I want to do. My MainActivity contains an extended adapter and a list of items:

public class MainActivity extends Activity
{
    private ArrayList<SliderItem> sliderItems;
    private SliderListAdapter adapter;

   // ...

    @Override
    protected void onCreate(Bundle savedInstanceState)
    {
        adapter = new SliderListAdapter(getApplicationContext(), sliderItems);
        sliderList.setAdapter(adapter);
    }
}

Every item contains a title, a count and a boolean to display it or not.

public class SliderItem 
{   
    private String title;
    private String count = "0";
    private boolean isCounterVisible = false;
    // ...
}

And my adapter handles the displaying of the items :

public class SliderListAdapter extends BaseAdapter 
{
    private Context context;
    private ArrayList<SliderItem> sliderItems;

    @Override
    public View getView(int position, View convertView, ViewGroup parent) 
    {
        TextView txtCount = (TextView) convertView.findViewById(R.id.counter);
        // ...

        if(sliderItems.get(position).isCounterVisible()){
            txtCount.setText(sliderItems.get(position).getCount());
        } else {
            txtCount.setVisibility(View.GONE);
        }
    }

    // ...
}

What I want to do now is to display a count after getting it from a webservice, so dynamically reload my ListView content. I know how to use AsyncTask and Services, but I don't know where to implement it... so what should I do? Thanks for your help.