Component does not render list with if statement

I am using mobx + react setup for this subpage to make a searchable list of users. My list of items is not rendering with if statement. In the solution I am trying to render one of two lists in my subpage. Depending on boolean 'isSearching'. First element should be shown when input field is empty, and second one is when input field has value written. They are same arrays, Only difference between lists arrays are that one of them is filtered.

<ul className='items__block'>
    {
    this.props.PeopleStore.people.isSearching = false //checks mobx prop
    ?
    (this.props.PeopleStore.people.map(this.person))
    : 
    (this.props.PeopleStore.searchingList.map(this.person))
    }
</ul>

Althought if I remove conditional if statement it works separated:

<ul className='items__block'>
    {
    this.props.PeopleStore.people.map(this.person)
    }
</ul>

-

<ul className='items__block'>
    {
    this.props.PeopleStore.people.map(this.person)
    }
</ul>

Store file:

import { runInAction, observable, action, toJS } from 'mobx';
// ES7 compiler
import regeneratorRuntime from 'regenerator-runtime';

class PeopleStore {
    @observable people = [];
    @observable loading = false;
    @observable isSearching = false;
    @observable searchingList = [];

// API call
loadPeople = async() => {
    this.loading = true;
    const response = await fetch('https://randomuser.me/api/?results=71');
    const json = await response.json();
    runInAction(() => {
        this.people = json.results;
    });
    this.loading = false;
    console.log(toJS(this.people));
}

// this function is called by onChange event
@action.bound filterList = textTyped => {
   // changing boolean to identify if input is empty or not
    if (textTyped.target.value.length < 1) {
        this.isSearching = false;
    } else {
        this.isSearching = true;
    }

    console.log(this.isSearching);

    let peoplesNames = [];
    for (let i = 0; i < this.people.length; i++) {
        peoplesNames.push(toJS(this.people[i]));
    }
    peoplesNames = peoplesNames.filter(function(item) {
        return item.name.first.toLowerCase().search(textTyped.target.value.toLowerCase()) !== -1
    });

    this.searchingList = peoplesNames;
// tracking both arrays, they both work
    console.log(toJS(this.searchingList));
    console.log(toJS(this.people));
    }
}

export default new PeopleStore();

Component file:

@inject('showHandler', 'PeopleStore') @observer
class PickList extends React.Component {

componentWillMount() {
    this.props.PeopleStore.loadPeople();
}


person = ({name, picture}, index) =>
    <li className="items__block--user" key={index} onClick={this.props.PeopleStore.selectPerson}>
        <img className="user--image" src={picture.medium} alt="face" />
        <span className="user--name">{`${name.first} ${name.last}`}</span>
    </li>;

render() {
    // loading screen
    if (this.props.PeopleStore.loading) {
        return (
            <div className="loader"></div>
        );
    }

    return (
        <React.Fragment>
            <input className="users__block--input" onChange={this.props.PeopleStore.filterList}></input>
            <ul className='items__block'>
                {
                this.props.PeopleStore.people.isSearching = false //checks mobx prop
                ?
                (this.props.PeopleStore.people.map(this.person))
                : 
                (this.props.PeopleStore.searchingList.map(this.person))
                }
            </ul>

Why is it not working? On page render isSearching prop is set to false and that should effect the if statement as it is.